1/y = Const - log(x) (уравнение)

Найду корень уравнения: 1/y = Const - log(x)

Вы ввели

1             
- = c - log(x)
y             

$$\frac{1}{y} = c - \log{\left(x \right)}$$

Подробное решение

Дано уравнение
$$\frac{1}{y} = c - \log{\left(x \right)}$$
Перенесём правую часть уравнения левую часть уравнения со знаком минус
$$\log{\left(x \right)} = c - \frac{1}{y}$$
Это уравнение вида:

log(v)=p

По определению log

v=e^p

тогда
$$x = e^{\frac{c - \frac{1}{y}}{1}}$$
упрощаем
$$x = e^{c - \frac{1}{y}}$$

Быстрый ответ

                                                                      re(y)         im(y)*im(c*y)     re(y)*re(c*y)              re(y)         im(y)*im(c*y)     re(y)*re(c*y)                                                          
                                                               - --------------- + --------------- + ---------------      - --------------- + --------------- + ---------------                                                         
                                                                   2        2        2        2        2        2             2        2        2        2        2        2                                                            
        /     im(y)         im(c*y)*re(y)     im(y)*re(c*y) \    im (y) + re (y)   im (y) + re (y)   im (y) + re (y)        im (y) + re (y)   im (y) + re (y)   im (y) + re (y)    /     im(y)         im(c*y)*re(y)     im(y)*re(c*y) \
x1 = cos|--------------- + --------------- - ---------------|*e                                                      + I*e                                                     *sin|--------------- + --------------- - ---------------|
        |  2        2        2        2        2        2   |                                                                                                                      |  2        2        2        2        2        2   |
        \im (y) + re (y)   im (y) + re (y)   im (y) + re (y)/                                                                                                                      \im (y) + re (y)   im (y) + re (y)   im (y) + re (y)/

$$x_{1} = i e^{\frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \sin{\left(\frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)} + e^{\frac{\operatorname{re}{\left(y\right)} \operatorname{re}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} \cos{\left(\frac{\operatorname{re}{\left(y\right)} \operatorname{im}{\left(c y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\operatorname{re}{\left(c y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}$$