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-y^1-y-log(y-1)=(c+1)/x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   1                    c + 1
- y  - y - log(y - 1) = -----
                          x
(−y1−y)−log⁡(y−1)=c+1x\left(- y^{1} - y\right) - \log{\left(y - 1 \right)} = \frac{c + 1}{x}
Simplificar
Solución detallada
Tenemos la ecuación:
(−y1−y)−log⁡(y−1)=c+1x\left(- y^{1} - y\right) - \log{\left(y - 1 \right)} = \frac{c + 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(-1 + y) - 2*y)

a2 = 1

b2 = x/(1 + c)

signo obtendremos la ecuación
xc+1=1−2y−log⁡(y−1)\frac{x}{c + 1} = \frac{1}{- 2 y - \log{\left(y - 1 \right)}}
xc+1=1−2y−log⁡(y−1)\frac{x}{c + 1} = \frac{1}{- 2 y - \log{\left(y - 1 \right)}}
Abrimos los paréntesis en el miembro izquierdo de la ecuación
x/1+/c = 1/(-log(-1 + y) - 2*y)

Abrimos los paréntesis en el miembro derecho de la ecuación
x/1+/c = -1/log-1/1+1/y - 2*y)

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
x/(1 + c) = -1/log-1/1+1/y - 2*y)

Dividamos ambos miembros de la ecuación en 1/(1 + c)
x = 1/(-log(-1 + y) - 2*y) / (1/(1 + c))

Obtenemos la respuesta: x = -(1 + c)/(2*y + log(-1 + y))
Gráfica
Respuesta rápida [src] 
       /           (1 + re(c))*(-arg(-1 + y) - 2*im(y))                      (2*re(y) + log(|-1 + y|))*im(c)           \               (-arg(-1 + y) - 2*im(y))*im(c)                      (1 + re(c))*(2*re(y) + log(|-1 + y|))        
x1 = I*|- ----------------------------------------------------- - -----------------------------------------------------| + ----------------------------------------------------- - -----------------------------------------------------
       |                         2                            2                          2                            2|                          2                            2                          2                            2
       \  (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))    (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|)) /   (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))    (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))
x1=i(−(log⁡(∣y−1∣)+2re⁡(y))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2−(re⁡(c)+1)(−2im⁡(y)−arg⁡(y−1))(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2)−(log⁡(∣y−1∣)+2re⁡(y))(re⁡(c)+1)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2+(−2im⁡(y)−arg⁡(y−1))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2x_{1} = i \left(- \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(c\right)} + 1\right) \left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}\right) - \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} + \frac{\left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} 
x1 = i*(-(log(|y - 1|) + 2*re(y))*im(c)/((log(|y - 1|) + 2*re(y))^2 + (2*im(y) + arg(y - 1))^2) - (re(c) + 1)*(-2*im(y) - arg(y - 1))/((log(|y - 1|) + 2*re(y))^2 + (2*im(y) + arg(y - 1))^2)) - (log(|y - 1|) + 2*re(y))*(re(c) + 1)/((log(|y - 1|) + 2*re(y))^2 + (2*im(y) + arg(y - 1))^2) + (-2*im(y) - arg(y - 1))*im(c)/((log(|y - 1|) + 2*re(y))^2 + (2*im(y) + arg(y - 1))^2)
Suma y producto de raíces [src] 
suma
  /           (1 + re(c))*(-arg(-1 + y) - 2*im(y))                      (2*re(y) + log(|-1 + y|))*im(c)           \               (-arg(-1 + y) - 2*im(y))*im(c)                      (1 + re(c))*(2*re(y) + log(|-1 + y|))        
I*|- ----------------------------------------------------- - -----------------------------------------------------| + ----------------------------------------------------- - -----------------------------------------------------
  |                         2                            2                          2                            2|                          2                            2                          2                            2
  \  (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))    (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|)) /   (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))    (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))
i(−(log⁡(∣y−1∣)+2re⁡(y))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2−(re⁡(c)+1)(−2im⁡(y)−arg⁡(y−1))(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2)−(log⁡(∣y−1∣)+2re⁡(y))(re⁡(c)+1)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2+(−2im⁡(y)−arg⁡(y−1))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2i \left(- \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(c\right)} + 1\right) \left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}\right) - \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} + \frac{\left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} 
=
  /           (1 + re(c))*(-arg(-1 + y) - 2*im(y))                      (2*re(y) + log(|-1 + y|))*im(c)           \               (-arg(-1 + y) - 2*im(y))*im(c)                      (1 + re(c))*(2*re(y) + log(|-1 + y|))        
I*|- ----------------------------------------------------- - -----------------------------------------------------| + ----------------------------------------------------- - -----------------------------------------------------
  |                         2                            2                          2                            2|                          2                            2                          2                            2
  \  (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))    (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|)) /   (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))    (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))
i(−(log⁡(∣y−1∣)+2re⁡(y))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2−(re⁡(c)+1)(−2im⁡(y)−arg⁡(y−1))(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2)−(log⁡(∣y−1∣)+2re⁡(y))(re⁡(c)+1)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2+(−2im⁡(y)−arg⁡(y−1))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2i \left(- \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(c\right)} + 1\right) \left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}\right) - \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} + \frac{\left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} 
producto
  /           (1 + re(c))*(-arg(-1 + y) - 2*im(y))                      (2*re(y) + log(|-1 + y|))*im(c)           \               (-arg(-1 + y) - 2*im(y))*im(c)                      (1 + re(c))*(2*re(y) + log(|-1 + y|))        
I*|- ----------------------------------------------------- - -----------------------------------------------------| + ----------------------------------------------------- - -----------------------------------------------------
  |                         2                            2                          2                            2|                          2                            2                          2                            2
  \  (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))    (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|)) /   (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))    (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))
i(−(log⁡(∣y−1∣)+2re⁡(y))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2−(re⁡(c)+1)(−2im⁡(y)−arg⁡(y−1))(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2)−(log⁡(∣y−1∣)+2re⁡(y))(re⁡(c)+1)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2+(−2im⁡(y)−arg⁡(y−1))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2i \left(- \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(c\right)} + 1\right) \left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}}\right) - \frac{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right)}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} + \frac{\left(- 2 \operatorname{im}{\left(y\right)} - \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} 
=
I*((1 + re(c))*(2*im(y) + arg(-1 + y)) - (2*re(y) + log(|-1 + y|))*im(c)) - (1 + re(c))*(2*re(y) + log(|-1 + y|)) - (2*im(y) + arg(-1 + y))*im(c)
-------------------------------------------------------------------------------------------------------------------------------------------------
                                                                     2                            2                                              
                                              (2*im(y) + arg(-1 + y))  + (2*re(y) + log(|-1 + y|))
i(−(log⁡(∣y−1∣)+2re⁡(y))im⁡(c)+(re⁡(c)+1)(2im⁡(y)+arg⁡(y−1)))−(log⁡(∣y−1∣)+2re⁡(y))(re⁡(c)+1)−(2im⁡(y)+arg⁡(y−1))im⁡(c)(log⁡(∣y−1∣)+2re⁡(y))2+(2im⁡(y)+arg⁡(y−1))2\frac{i \left(- \left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(c\right)} + \left(\operatorname{re}{\left(c\right)} + 1\right) \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)\right) - \left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + 1\right) - \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right) \operatorname{im}{\left(c\right)}}{\left(\log{\left(\left|{y - 1}\right| \right)} + 2 \operatorname{re}{\left(y\right)}\right)^{2} + \left(2 \operatorname{im}{\left(y\right)} + \arg{\left(y - 1 \right)}\right)^{2}} 
(i*((1 + re(c))*(2*im(y) + arg(-1 + y)) - (2*re(y) + log(|-1 + y|))*im(c)) - (1 + re(c))*(2*re(y) + log(|-1 + y|)) - (2*im(y) + arg(-1 + y))*im(c))/((2*im(y) + arg(-1 + y))^2 + (2*re(y) + log(|-1 + y|))^2)
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