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lny=(-1/x)+lnc la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
           1         
log(y) = - - + log(c)
           x
log⁡(y)=log⁡(c)−1x\log{\left(y \right)} = \log{\left(c \right)} - \frac{1}{x}
Simplificar
Solución detallada
Tenemos la ecuación:
log⁡(y)=log⁡(c)−1x\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=1−log⁡(c)+log⁡(y)- x = \frac{1}{- \log{\left(c \right)} + \log{\left(y \right)}}
−x=1−log⁡(c)+log⁡(y)- 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))
Gráfica
Respuesta rápida [src] 
                  -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|))
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))2x_{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] 
suma
             -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|))
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\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|))
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\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}} 
producto
             -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|))
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\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|))
i(−arg⁡(c)+arg⁡(y))+log⁡(∣c∣)−log⁡(∣y∣)(log⁡(∣c∣)−log⁡(∣y∣))2+(arg⁡(c)−arg⁡(y))2\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)
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