(e^(38*x))-1=100000 (уравнение)

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Найду корень уравнения: (e^(38*x))-1=100000

Решение

Вы ввели [src]

 38*x             
E     - 1 = 100000

$$e^{38 x} - 1 = 100000$$

Упростить

Подробное решение

Дано уравнение:
$$e^{38 x} - 1 = 100000$$
или
$$\left(e^{38 x} - 1\right) - 100000 = 0$$
или
$$e^{38 x} = 100001$$
или
$$e^{38 x} = 100001$$
- это простейшее показательное ур-ние
Сделаем замену
$$v = e^{38 x}$$
получим
$$v - 100001 = 0$$
или
$$v - 100001 = 0$$
Переносим свободные слагаемые (без v)
из левой части в правую, получим:
$$v = 100001$$
Получим ответ: v = 100001
делаем обратную замену
$$e^{38 x} = v$$
или
$$x = \frac{\log{\left(v \right)}}{38}$$
Тогда, окончательный ответ
$$x_{1} = \frac{\log{\left(100001 \right)}}{\log{\left(e^{38} \right)}} = \frac{\log{\left(100001 \right)}}{38}$$

График

Построить график f1(x)

Построить график f2(x)

Быстрый ответ [src]

        /38________\
x1 = log\\/ 100001 /

$$x_{1} = \log{\left(\sqrt[38]{100001} \right)}$$

               /38________\
x2 = pi*I + log\\/ 100001 /

$$x_{2} = \log{\left(\sqrt[38]{100001} \right)} + i \pi$$

       /          /   /pi\\\                                                       
       |          |sin|--|||      /    ___________________________________________\
       |          |   \19/||      |   / 19________    2/pi\   19________    2/pi\ |
x3 = I*|-pi + atan|-------|| + log|  /  \/ 100001 *cos |--| + \/ 100001 *sin |--| |
       |          |   /pi\||      \\/                  \19/                  \19/ /
       |          |cos|--|||                                                       
       \          \   \19///

$$x_{3} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{\pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{\pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{19} \right)}}{\cos{\left(\frac{\pi}{19} \right)}} \right)}\right)$$

       /         /   /pi\\\                                                       
       |         |sin|--|||      /    ___________________________________________\
       |         |   \19/||      |   / 19________    2/pi\   19________    2/pi\ |
x4 = I*|pi - atan|-------|| + log|  /  \/ 100001 *cos |--| + \/ 100001 *sin |--| |
       |         |   /pi\||      \\/                  \19/                  \19/ /
       |         |cos|--|||                                                       
       \         \   \19///

$$x_{4} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{\pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{\pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{19} \right)}}{\cos{\left(\frac{\pi}{19} \right)}} \right)}\right)$$

             /   /pi\\                                                       
             |sin|--||      /    ___________________________________________\
             |   \19/|      |   / 19________    2/pi\   19________    2/pi\ |
x5 = - I*atan|-------| + log|  /  \/ 100001 *cos |--| + \/ 100001 *sin |--| |
             |   /pi\|      \\/                  \19/                  \19/ /
             |cos|--||                                                       
             \   \19//

$$x_{5} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{\pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{\pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{19} \right)}}{\cos{\left(\frac{\pi}{19} \right)}} \right)}$$

           /   /pi\\                                                       
           |sin|--||      /    ___________________________________________\
           |   \19/|      |   / 19________    2/pi\   19________    2/pi\ |
x6 = I*atan|-------| + log|  /  \/ 100001 *cos |--| + \/ 100001 *sin |--| |
           |   /pi\|      \\/                  \19/                  \19/ /
           |cos|--||                                                       
           \   \19//

$$x_{6} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{\pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{\pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{\pi}{19} \right)}}{\cos{\left(\frac{\pi}{19} \right)}} \right)}$$

       /          /   /2*pi\\\                                                           
       |          |sin|----|||      /    _______________________________________________\
       |          |   \ 19 /||      |   / 19________    2/2*pi\   19________    2/2*pi\ |
x7 = I*|-pi + atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
       |          |   /2*pi\||      \\/                  \ 19 /                  \ 19 / /
       |          |cos|----|||                                                           
       \          \   \ 19 ///

$$x_{7} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{2 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{2 \pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{19} \right)}}{\cos{\left(\frac{2 \pi}{19} \right)}} \right)}\right)$$

       /         /   /2*pi\\\                                                           
       |         |sin|----|||      /    _______________________________________________\
       |         |   \ 19 /||      |   / 19________    2/2*pi\   19________    2/2*pi\ |
x8 = I*|pi - atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
       |         |   /2*pi\||      \\/                  \ 19 /                  \ 19 / /
       |         |cos|----|||                                                           
       \         \   \ 19 ///

$$x_{8} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{2 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{2 \pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{19} \right)}}{\cos{\left(\frac{2 \pi}{19} \right)}} \right)}\right)$$

             /   /2*pi\\                                                           
             |sin|----||      /    _______________________________________________\
             |   \ 19 /|      |   / 19________    2/2*pi\   19________    2/2*pi\ |
x9 = - I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
             |   /2*pi\|      \\/                  \ 19 /                  \ 19 / /
             |cos|----||                                                           
             \   \ 19 //

$$x_{9} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{2 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{2 \pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{19} \right)}}{\cos{\left(\frac{2 \pi}{19} \right)}} \right)}$$

            /   /2*pi\\                                                           
            |sin|----||      /    _______________________________________________\
            |   \ 19 /|      |   / 19________    2/2*pi\   19________    2/2*pi\ |
x10 = I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
            |   /2*pi\|      \\/                  \ 19 /                  \ 19 / /
            |cos|----||                                                           
            \   \ 19 //

$$x_{10} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{2 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{2 \pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{2 \pi}{19} \right)}}{\cos{\left(\frac{2 \pi}{19} \right)}} \right)}$$

        /          /   /3*pi\\\                                                           
        |          |sin|----|||      /    _______________________________________________\
        |          |   \ 19 /||      |   / 19________    2/3*pi\   19________    2/3*pi\ |
x11 = I*|-pi + atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |          |   /3*pi\||      \\/                  \ 19 /                  \ 19 / /
        |          |cos|----|||                                                           
        \          \   \ 19 ///

$$x_{11} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{3 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{3 \pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{19} \right)}}{\cos{\left(\frac{3 \pi}{19} \right)}} \right)}\right)$$

        /         /   /3*pi\\\                                                           
        |         |sin|----|||      /    _______________________________________________\
        |         |   \ 19 /||      |   / 19________    2/3*pi\   19________    2/3*pi\ |
x12 = I*|pi - atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |         |   /3*pi\||      \\/                  \ 19 /                  \ 19 / /
        |         |cos|----|||                                                           
        \         \   \ 19 ///

$$x_{12} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{3 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{3 \pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{19} \right)}}{\cos{\left(\frac{3 \pi}{19} \right)}} \right)}\right)$$

              /   /3*pi\\                                                           
              |sin|----||      /    _______________________________________________\
              |   \ 19 /|      |   / 19________    2/3*pi\   19________    2/3*pi\ |
x13 = - I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
              |   /3*pi\|      \\/                  \ 19 /                  \ 19 / /
              |cos|----||                                                           
              \   \ 19 //

$$x_{13} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{3 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{3 \pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{19} \right)}}{\cos{\left(\frac{3 \pi}{19} \right)}} \right)}$$

            /   /3*pi\\                                                           
            |sin|----||      /    _______________________________________________\
            |   \ 19 /|      |   / 19________    2/3*pi\   19________    2/3*pi\ |
x14 = I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
            |   /3*pi\|      \\/                  \ 19 /                  \ 19 / /
            |cos|----||                                                           
            \   \ 19 //

$$x_{14} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{3 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{3 \pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{19} \right)}}{\cos{\left(\frac{3 \pi}{19} \right)}} \right)}$$

        /          /   /4*pi\\\                                                           
        |          |sin|----|||      /    _______________________________________________\
        |          |   \ 19 /||      |   / 19________    2/4*pi\   19________    2/4*pi\ |
x15 = I*|-pi + atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |          |   /4*pi\||      \\/                  \ 19 /                  \ 19 / /
        |          |cos|----|||                                                           
        \          \   \ 19 ///

$$x_{15} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{4 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{4 \pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{4 \pi}{19} \right)}}{\cos{\left(\frac{4 \pi}{19} \right)}} \right)}\right)$$

        /         /   /4*pi\\\                                                           
        |         |sin|----|||      /    _______________________________________________\
        |         |   \ 19 /||      |   / 19________    2/4*pi\   19________    2/4*pi\ |
x16 = I*|pi - atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |         |   /4*pi\||      \\/                  \ 19 /                  \ 19 / /
        |         |cos|----|||                                                           
        \         \   \ 19 ///

$$x_{16} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{4 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{4 \pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{4 \pi}{19} \right)}}{\cos{\left(\frac{4 \pi}{19} \right)}} \right)}\right)$$

              /   /4*pi\\                                                           
              |sin|----||      /    _______________________________________________\
              |   \ 19 /|      |   / 19________    2/4*pi\   19________    2/4*pi\ |
x17 = - I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
              |   /4*pi\|      \\/                  \ 19 /                  \ 19 / /
              |cos|----||                                                           
              \   \ 19 //

$$x_{17} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{4 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{4 \pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{4 \pi}{19} \right)}}{\cos{\left(\frac{4 \pi}{19} \right)}} \right)}$$

            /   /4*pi\\                                                           
            |sin|----||      /    _______________________________________________\
            |   \ 19 /|      |   / 19________    2/4*pi\   19________    2/4*pi\ |
x18 = I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
            |   /4*pi\|      \\/                  \ 19 /                  \ 19 / /
            |cos|----||                                                           
            \   \ 19 //

$$x_{18} = \log{\left(\sqrt{\sqrt[19]{100001} \sin^{2}{\left(\frac{4 \pi}{19} \right)} + \sqrt[19]{100001} \cos^{2}{\left(\frac{4 \pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{4 \pi}{19} \right)}}{\cos{\left(\frac{4 \pi}{19} \right)}} \right)}$$

        /          /   /5*pi\\\                                                           
        |          |sin|----|||      /    _______________________________________________\
        |          |   \ 19 /||      |   / 19________    2/5*pi\   19________    2/5*pi\ |
x19 = I*|-pi + atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |          |   /5*pi\||      \\/                  \ 19 /                  \ 19 / /
        |          |cos|----|||                                                           
        \          \   \ 19 ///

$$x_{19} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{5 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{5 \pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{19} \right)}}{\cos{\left(\frac{5 \pi}{19} \right)}} \right)}\right)$$

        /         /   /5*pi\\\                                                           
        |         |sin|----|||      /    _______________________________________________\
        |         |   \ 19 /||      |   / 19________    2/5*pi\   19________    2/5*pi\ |
x20 = I*|pi - atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |         |   /5*pi\||      \\/                  \ 19 /                  \ 19 / /
        |         |cos|----|||                                                           
        \         \   \ 19 ///

$$x_{20} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{5 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{5 \pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{19} \right)}}{\cos{\left(\frac{5 \pi}{19} \right)}} \right)}\right)$$

              /   /5*pi\\                                                           
              |sin|----||      /    _______________________________________________\
              |   \ 19 /|      |   / 19________    2/5*pi\   19________    2/5*pi\ |
x21 = - I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
              |   /5*pi\|      \\/                  \ 19 /                  \ 19 / /
              |cos|----||                                                           
              \   \ 19 //

$$x_{21} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{5 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{5 \pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{19} \right)}}{\cos{\left(\frac{5 \pi}{19} \right)}} \right)}$$

            /   /5*pi\\                                                           
            |sin|----||      /    _______________________________________________\
            |   \ 19 /|      |   / 19________    2/5*pi\   19________    2/5*pi\ |
x22 = I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
            |   /5*pi\|      \\/                  \ 19 /                  \ 19 / /
            |cos|----||                                                           
            \   \ 19 //

$$x_{22} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{5 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{5 \pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{19} \right)}}{\cos{\left(\frac{5 \pi}{19} \right)}} \right)}$$

        /          /   /6*pi\\\                                                           
        |          |sin|----|||      /    _______________________________________________\
        |          |   \ 19 /||      |   / 19________    2/6*pi\   19________    2/6*pi\ |
x23 = I*|-pi + atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |          |   /6*pi\||      \\/                  \ 19 /                  \ 19 / /
        |          |cos|----|||                                                           
        \          \   \ 19 ///

$$x_{23} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{6 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{6 \pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{6 \pi}{19} \right)}}{\cos{\left(\frac{6 \pi}{19} \right)}} \right)}\right)$$

        /         /   /6*pi\\\                                                           
        |         |sin|----|||      /    _______________________________________________\
        |         |   \ 19 /||      |   / 19________    2/6*pi\   19________    2/6*pi\ |
x24 = I*|pi - atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |         |   /6*pi\||      \\/                  \ 19 /                  \ 19 / /
        |         |cos|----|||                                                           
        \         \   \ 19 ///

$$x_{24} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{6 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{6 \pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{6 \pi}{19} \right)}}{\cos{\left(\frac{6 \pi}{19} \right)}} \right)}\right)$$

              /   /6*pi\\                                                           
              |sin|----||      /    _______________________________________________\
              |   \ 19 /|      |   / 19________    2/6*pi\   19________    2/6*pi\ |
x25 = - I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
              |   /6*pi\|      \\/                  \ 19 /                  \ 19 / /
              |cos|----||                                                           
              \   \ 19 //

$$x_{25} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{6 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{6 \pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{6 \pi}{19} \right)}}{\cos{\left(\frac{6 \pi}{19} \right)}} \right)}$$

            /   /6*pi\\                                                           
            |sin|----||      /    _______________________________________________\
            |   \ 19 /|      |   / 19________    2/6*pi\   19________    2/6*pi\ |
x26 = I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
            |   /6*pi\|      \\/                  \ 19 /                  \ 19 / /
            |cos|----||                                                           
            \   \ 19 //

$$x_{26} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{6 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{6 \pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{6 \pi}{19} \right)}}{\cos{\left(\frac{6 \pi}{19} \right)}} \right)}$$

        /          /   /7*pi\\\                                                           
        |          |sin|----|||      /    _______________________________________________\
        |          |   \ 19 /||      |   / 19________    2/7*pi\   19________    2/7*pi\ |
x27 = I*|-pi + atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |          |   /7*pi\||      \\/                  \ 19 /                  \ 19 / /
        |          |cos|----|||                                                           
        \          \   \ 19 ///

$$x_{27} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{7 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{7 \pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{7 \pi}{19} \right)}}{\cos{\left(\frac{7 \pi}{19} \right)}} \right)}\right)$$

        /         /   /7*pi\\\                                                           
        |         |sin|----|||      /    _______________________________________________\
        |         |   \ 19 /||      |   / 19________    2/7*pi\   19________    2/7*pi\ |
x28 = I*|pi - atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |         |   /7*pi\||      \\/                  \ 19 /                  \ 19 / /
        |         |cos|----|||                                                           
        \         \   \ 19 ///

$$x_{28} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{7 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{7 \pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{7 \pi}{19} \right)}}{\cos{\left(\frac{7 \pi}{19} \right)}} \right)}\right)$$

              /   /7*pi\\                                                           
              |sin|----||      /    _______________________________________________\
              |   \ 19 /|      |   / 19________    2/7*pi\   19________    2/7*pi\ |
x29 = - I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
              |   /7*pi\|      \\/                  \ 19 /                  \ 19 / /
              |cos|----||                                                           
              \   \ 19 //

$$x_{29} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{7 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{7 \pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{7 \pi}{19} \right)}}{\cos{\left(\frac{7 \pi}{19} \right)}} \right)}$$

            /   /7*pi\\                                                           
            |sin|----||      /    _______________________________________________\
            |   \ 19 /|      |   / 19________    2/7*pi\   19________    2/7*pi\ |
x30 = I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
            |   /7*pi\|      \\/                  \ 19 /                  \ 19 / /
            |cos|----||                                                           
            \   \ 19 //

$$x_{30} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{7 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{7 \pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{7 \pi}{19} \right)}}{\cos{\left(\frac{7 \pi}{19} \right)}} \right)}$$

        /          /   /8*pi\\\                                                           
        |          |sin|----|||      /    _______________________________________________\
        |          |   \ 19 /||      |   / 19________    2/8*pi\   19________    2/8*pi\ |
x31 = I*|-pi + atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |          |   /8*pi\||      \\/                  \ 19 /                  \ 19 / /
        |          |cos|----|||                                                           
        \          \   \ 19 ///

$$x_{31} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{8 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{8 \pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{8 \pi}{19} \right)}}{\cos{\left(\frac{8 \pi}{19} \right)}} \right)}\right)$$

        /         /   /8*pi\\\                                                           
        |         |sin|----|||      /    _______________________________________________\
        |         |   \ 19 /||      |   / 19________    2/8*pi\   19________    2/8*pi\ |
x32 = I*|pi - atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |         |   /8*pi\||      \\/                  \ 19 /                  \ 19 / /
        |         |cos|----|||                                                           
        \         \   \ 19 ///

$$x_{32} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{8 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{8 \pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{8 \pi}{19} \right)}}{\cos{\left(\frac{8 \pi}{19} \right)}} \right)}\right)$$

              /   /8*pi\\                                                           
              |sin|----||      /    _______________________________________________\
              |   \ 19 /|      |   / 19________    2/8*pi\   19________    2/8*pi\ |
x33 = - I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
              |   /8*pi\|      \\/                  \ 19 /                  \ 19 / /
              |cos|----||                                                           
              \   \ 19 //

$$x_{33} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{8 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{8 \pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{8 \pi}{19} \right)}}{\cos{\left(\frac{8 \pi}{19} \right)}} \right)}$$

            /   /8*pi\\                                                           
            |sin|----||      /    _______________________________________________\
            |   \ 19 /|      |   / 19________    2/8*pi\   19________    2/8*pi\ |
x34 = I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
            |   /8*pi\|      \\/                  \ 19 /                  \ 19 / /
            |cos|----||                                                           
            \   \ 19 //

$$x_{34} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{8 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{8 \pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{8 \pi}{19} \right)}}{\cos{\left(\frac{8 \pi}{19} \right)}} \right)}$$

        /          /   /9*pi\\\                                                           
        |          |sin|----|||      /    _______________________________________________\
        |          |   \ 19 /||      |   / 19________    2/9*pi\   19________    2/9*pi\ |
x35 = I*|-pi + atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |          |   /9*pi\||      \\/                  \ 19 /                  \ 19 / /
        |          |cos|----|||                                                           
        \          \   \ 19 ///

$$x_{35} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{9 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{9 \pi}{19} \right)}} \right)} + i \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{9 \pi}{19} \right)}}{\cos{\left(\frac{9 \pi}{19} \right)}} \right)}\right)$$

        /         /   /9*pi\\\                                                           
        |         |sin|----|||      /    _______________________________________________\
        |         |   \ 19 /||      |   / 19________    2/9*pi\   19________    2/9*pi\ |
x36 = I*|pi - atan|---------|| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
        |         |   /9*pi\||      \\/                  \ 19 /                  \ 19 / /
        |         |cos|----|||                                                           
        \         \   \ 19 ///

$$x_{36} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{9 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{9 \pi}{19} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{9 \pi}{19} \right)}}{\cos{\left(\frac{9 \pi}{19} \right)}} \right)}\right)$$

              /   /9*pi\\                                                           
              |sin|----||      /    _______________________________________________\
              |   \ 19 /|      |   / 19________    2/9*pi\   19________    2/9*pi\ |
x37 = - I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
              |   /9*pi\|      \\/                  \ 19 /                  \ 19 / /
              |cos|----||                                                           
              \   \ 19 //

$$x_{37} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{9 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{9 \pi}{19} \right)}} \right)} - i \operatorname{atan}{\left(\frac{\sin{\left(\frac{9 \pi}{19} \right)}}{\cos{\left(\frac{9 \pi}{19} \right)}} \right)}$$

            /   /9*pi\\                                                           
            |sin|----||      /    _______________________________________________\
            |   \ 19 /|      |   / 19________    2/9*pi\   19________    2/9*pi\ |
x38 = I*atan|---------| + log|  /  \/ 100001 *cos |----| + \/ 100001 *sin |----| |
            |   /9*pi\|      \\/                  \ 19 /                  \ 19 / /
            |cos|----||                                                           
            \   \ 19 //

$$x_{38} = \log{\left(\sqrt{\sqrt[19]{100001} \cos^{2}{\left(\frac{9 \pi}{19} \right)} + \sqrt[19]{100001} \sin^{2}{\left(\frac{9 \pi}{19} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{9 \pi}{19} \right)}}{\cos{\left(\frac{9 \pi}{19} \right)}} \right)}$$

Численный ответ [src]

x1 = 0.302971985918953 + 3.14159265358979*i

x2 = 0.302971985918953

x3 = 0.302971985918953 - 2.97624567182191*i

x4 = 0.302971985918953 + 2.97624567182191*i

x5 = 0.302971985918953 - 0.165346981767884*i

x6 = 0.302971985918953 + 0.165346981767884*i

x7 = 0.302971985918953 - 2.81089869005403*i

x8 = 0.302971985918953 + 2.81089869005403*i

x9 = 0.302971985918953 - 0.330693963535768*i

x10 = 0.302971985918953 + 0.330693963535768*i

x11 = 0.302971985918953 - 2.64555170828614*i

x12 = 0.302971985918953 + 2.64555170828614*i

x13 = 0.302971985918953 - 0.496040945303652*i

x14 = 0.302971985918953 + 0.496040945303652*i

x15 = 0.302971985918953 - 2.48020472651826*i

x16 = 0.302971985918953 + 2.48020472651826*i

x17 = 0.302971985918953 - 0.661387927071535*i

x18 = 0.302971985918953 + 0.661387927071535*i

x19 = 0.302971985918953 - 2.31485774475037*i

x20 = 0.302971985918953 + 2.31485774475037*i

x21 = 0.302971985918953 - 0.826734908839419*i

x22 = 0.302971985918953 + 0.826734908839419*i

x23 = 0.302971985918953 - 2.14951076298249*i

x24 = 0.302971985918953 + 2.14951076298249*i

x25 = 0.302971985918953 - 0.992081890607303*i

x26 = 0.302971985918953 + 0.992081890607303*i

x27 = 0.302971985918953 - 1.98416378121461*i

x28 = 0.302971985918953 + 1.98416378121461*i

x29 = 0.302971985918953 - 1.15742887237519*i

x30 = 0.302971985918953 + 1.15742887237519*i

x31 = 0.302971985918953 - 1.81881679944672*i

x32 = 0.302971985918953 + 1.81881679944672*i

x33 = 0.302971985918953 - 1.32277585414307*i

x34 = 0.302971985918953 + 1.32277585414307*i

x35 = 0.302971985918953 - 1.65346981767884*i

x36 = 0.302971985918953 + 1.65346981767884*i

x37 = 0.302971985918953 - 1.48812283591095*i

x38 = 0.302971985918953 + 1.48812283591095*i

График

(e^(38*x))-1=100000 (уравнение) /media/krcore-image-pods/hash/equation/a/de/b8699534f9d5f17eb063d0bc65613.png

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(e^(38*x))-1=100000 (уравнение)

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