5^(4*x+1)=25^x (уравнение)

Найду корень уравнения: 5^(4*x+1)=25^x

Вы ввели

 4*x + 1     x
5        = 25 

$$5^{4 x + 1} = 25^{x}$$

Сумма и произведение корней

сумма

            1    pi*I 
0 - 1/2 + - - + ------
            2   log(5)

$$\left(- \frac{1}{2} + 0\right) - \left(\frac{1}{2} - \frac{i \pi}{\log{\left(5 \right)}}\right)$$

=

      pi*I 
-1 + ------
     log(5)

$$-1 + \frac{i \pi}{\log{\left(5 \right)}}$$

произведение

       /  1    pi*I \
1*-1/2*|- - + ------|
       \  2   log(5)/

$$1 \left(- \frac{1}{2}\right) \left(- \frac{1}{2} + \frac{i \pi}{\log{\left(5 \right)}}\right)$$

=

1     pi*I  
- - --------
4   2*log(5)

$$\frac{1}{4} - \frac{i \pi}{2 \log{\left(5 \right)}}$$

Быстрый ответ

x1 = -1/2

$$x_{1} = - \frac{1}{2}$$

       1    pi*I 
x2 = - - + ------
       2   log(5)

$$x_{2} = - \frac{1}{2} + \frac{i \pi}{\log{\left(5 \right)}}$$

Численный ответ

x1 = -68.3923009482611

x2 = -46.3923009482611

x3 = -18.3923009482611

x4 = -26.3923009482611

x5 = -86.3923009482611

x6 = -98.3923009482611

x7 = -36.3923009482611

x8 = -38.3923009482611

x9 = -72.3923009482611

x10 = -16.3923009482611

x11 = -66.3923009482611

x12 = -12.3923009640351

x13 = -14.3923009482863

x14 = -94.3923009482611

x15 = -24.3923009482611

x16 = -104.392300948261

x17 = -32.3923009482611

x18 = -0.5

x19 = -48.3923009482611

x20 = -42.3923009482611

x21 = -64.3923009482611

x22 = -82.3923009482611

x23 = -96.3923009482611

x24 = -100.392300948261

x25 = -20.3923009482611

x26 = -56.3923009482611

x27 = -34.3923009482611

x28 = -22.3923009482611

x29 = -88.3923009482611

x30 = -106.392300948261

x31 = -62.3923009482611

x32 = -76.3923009482611

x33 = -28.3923009482611

x34 = -10.3923108072624

x35 = -74.3923009482611

x36 = -78.3923009482611

x37 = -102.392300948261

x38 = -40.3923009482611

x39 = -54.3923009482611

x40 = -58.3923009482611

x41 = -44.3923009482611

x42 = -30.3923009482611

x43 = -70.3923009482611

x44 = -50.3923009482611

x45 = -60.3923009482611

x46 = -92.3923009482611

x47 = -90.3923009482611

x48 = -52.3923009482611

x49 = -80.3923009482611

x50 = -84.3923009482611

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