Solución detallada
Tenemos la ecuación:
$$\log{\left(y \right)} = \log{\left(c \right)} - \frac{1}{x}$$
Usamos la regla de proporciones:
De a1/b1 = a2/b2 se deduce a1*b2 = a2*b1,
En nuestro caso
a1 = 1
b1 = 1/(-log(c) + log(y))
a2 = 1
b2 = -x
signo obtendremos la ecuación
$$- x = \frac{1}{- \log{\left(c \right)} + \log{\left(y \right)}}$$
$$- x = \frac{1}{- \log{\left(c \right)} + \log{\left(y \right)}}$$
Abrimos los paréntesis en el miembro derecho de la ecuación
-x = -1/log+1/c + logy)
Dividamos ambos miembros de la ecuación en -1
x = 1/(-log(c) + log(y)) / (-1)
Obtenemos la respuesta: x = 1/(-log(y) + log(c))
-log(|y|) + log(|c|) I*(-arg(c) + arg(y))
x1 = --------------------------------------------- + ---------------------------------------------
2 2 2 2
(-arg(y) + arg(c)) + (-log(|y|) + log(|c|)) (-arg(y) + arg(c)) + (-log(|y|) + log(|c|))
$$x_{1} = \frac{\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}} + \frac{i \left(- \arg{\left(c \right)} + \arg{\left(y \right)}\right)}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}}$$
x1 = (log(|c|) - log(|y|))/((log(|c|) - log(|y|))^2 + (arg(c) - arg(y))^2) + i*(-arg(c) + arg(y))/((log(|c|) - log(|y|))^2 + (arg(c) - arg(y))^2)
Suma y producto de raíces
[src]
-log(|y|) + log(|c|) I*(-arg(c) + arg(y))
--------------------------------------------- + ---------------------------------------------
2 2 2 2
(-arg(y) + arg(c)) + (-log(|y|) + log(|c|)) (-arg(y) + arg(c)) + (-log(|y|) + log(|c|))
$$\frac{\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}} + \frac{i \left(- \arg{\left(c \right)} + \arg{\left(y \right)}\right)}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}}$$
-log(|y|) + log(|c|) I*(-arg(c) + arg(y))
--------------------------------------------- + ---------------------------------------------
2 2 2 2
(-arg(y) + arg(c)) + (-log(|y|) + log(|c|)) (-arg(y) + arg(c)) + (-log(|y|) + log(|c|))
$$\frac{\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}} + \frac{i \left(- \arg{\left(c \right)} + \arg{\left(y \right)}\right)}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}}$$
-log(|y|) + log(|c|) I*(-arg(c) + arg(y))
--------------------------------------------- + ---------------------------------------------
2 2 2 2
(-arg(y) + arg(c)) + (-log(|y|) + log(|c|)) (-arg(y) + arg(c)) + (-log(|y|) + log(|c|))
$$\frac{\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}} + \frac{i \left(- \arg{\left(c \right)} + \arg{\left(y \right)}\right)}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}}$$
-log(|y|) + I*(-arg(c) + arg(y)) + log(|c|)
---------------------------------------------
2 2
(-arg(y) + arg(c)) + (-log(|y|) + log(|c|))
$$\frac{i \left(- \arg{\left(c \right)} + \arg{\left(y \right)}\right) + \log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}}{\left(\log{\left(\left|{c}\right| \right)} - \log{\left(\left|{y}\right| \right)}\right)^{2} + \left(\arg{\left(c \right)} - \arg{\left(y \right)}\right)^{2}}$$
(-log(|y|) + i*(-arg(c) + arg(y)) + log(|c|))/((-arg(y) + arg(c))^2 + (-log(|y|) + log(|c|))^2)