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log(y^2-2)=c+1/x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   / 2    \       1
log\y  - 2/ = c + -
                  x
log⁡(y2−2)=c+1x\log{\left(y^{2} - 2 \right)} = c + \frac{1}{x}
Simplificar
Solución detallada
Tenemos la ecuación:
log⁡(y2−2)=c+1x\log{\left(y^{2} - 2 \right)} = c + \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/(-c + log(-2 + y^2))

a2 = 1

b2 = x

signo obtendremos la ecuación
x=1−c+log⁡(y2−2)x = \frac{1}{- c + \log{\left(y^{2} - 2 \right)}}
x=1−c+log⁡(y2−2)x = \frac{1}{- c + \log{\left(y^{2} - 2 \right)}}
Abrimos los paréntesis en el miembro derecho de la ecuación
x = -1/c+1/log-1/2+1/y+1/2)

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

Obtenemos la respuesta: x = -1/(c - log(-2 + y^2))
Gráfica
Respuesta rápida [src] 
                            /|      2|\                                           /            /      2\\               
                       - log\|-2 + y |/ + re(c)                                 I*\-im(c) + arg\-2 + y //               
x1 = - ------------------------------------------------------- - -------------------------------------------------------
                               2                             2                           2                             2
       /     /      2\        \    /     /|      2|\        \    /     /      2\        \    /     /|      2|\        \ 
       \- arg\-2 + y / + im(c)/  + \- log\|-2 + y |/ + re(c)/    \- arg\-2 + y / + im(c)/  + \- log\|-2 + y |/ + re(c)/
x1=−−log⁡(∣y2−2∣)+re⁡(c)(−log⁡(∣y2−2∣)+re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2−i(−im⁡(c)+arg⁡(y2−2))(−log⁡(∣y2−2∣)+re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2x_{1} = - \frac{- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}}{\left(- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} - \frac{i \left(- \operatorname{im}{\left(c\right)} + \arg{\left(y^{2} - 2 \right)}\right)}{\left(- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} 
x1 = -(-log(|y^2 - 2|) + re(c))/((-log(|y^2 - 2|) + re(c))^2 + (im(c) - arg(y^2 - 2))^2) - i*(-im(c) + arg(y^2 - 2))/((-log(|y^2 - 2|) + re(c))^2 + (im(c) - arg(y^2 - 2))^2)
Suma y producto de raíces [src] 
suma
                       /|      2|\                                           /            /      2\\               
                  - log\|-2 + y |/ + re(c)                                 I*\-im(c) + arg\-2 + y //               
- ------------------------------------------------------- - -------------------------------------------------------
                          2                             2                           2                             2
  /     /      2\        \    /     /|      2|\        \    /     /      2\        \    /     /|      2|\        \ 
  \- arg\-2 + y / + im(c)/  + \- log\|-2 + y |/ + re(c)/    \- arg\-2 + y / + im(c)/  + \- log\|-2 + y |/ + re(c)/
−−log⁡(∣y2−2∣)+re⁡(c)(−log⁡(∣y2−2∣)+re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2−i(−im⁡(c)+arg⁡(y2−2))(−log⁡(∣y2−2∣)+re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2- \frac{- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}}{\left(- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} - \frac{i \left(- \operatorname{im}{\left(c\right)} + \arg{\left(y^{2} - 2 \right)}\right)}{\left(- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} 
=
                       /|      2|\                                           /            /      2\\               
                  - log\|-2 + y |/ + re(c)                                 I*\-im(c) + arg\-2 + y //               
- ------------------------------------------------------- - -------------------------------------------------------
                          2                             2                           2                             2
  /     /      2\        \    /     /|      2|\        \    /     /      2\        \    /     /|      2|\        \ 
  \- arg\-2 + y / + im(c)/  + \- log\|-2 + y |/ + re(c)/    \- arg\-2 + y / + im(c)/  + \- log\|-2 + y |/ + re(c)/
−−log⁡(∣y2−2∣)+re⁡(c)(−log⁡(∣y2−2∣)+re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2−i(−im⁡(c)+arg⁡(y2−2))(−log⁡(∣y2−2∣)+re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2- \frac{- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}}{\left(- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} - \frac{i \left(- \operatorname{im}{\left(c\right)} + \arg{\left(y^{2} - 2 \right)}\right)}{\left(- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} 
producto
                       /|      2|\                                           /            /      2\\               
                  - log\|-2 + y |/ + re(c)                                 I*\-im(c) + arg\-2 + y //               
- ------------------------------------------------------- - -------------------------------------------------------
                          2                             2                           2                             2
  /     /      2\        \    /     /|      2|\        \    /     /      2\        \    /     /|      2|\        \ 
  \- arg\-2 + y / + im(c)/  + \- log\|-2 + y |/ + re(c)/    \- arg\-2 + y / + im(c)/  + \- log\|-2 + y |/ + re(c)/
−−log⁡(∣y2−2∣)+re⁡(c)(−log⁡(∣y2−2∣)+re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2−i(−im⁡(c)+arg⁡(y2−2))(−log⁡(∣y2−2∣)+re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2- \frac{- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}}{\left(- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} - \frac{i \left(- \operatorname{im}{\left(c\right)} + \arg{\left(y^{2} - 2 \right)}\right)}{\left(- \log{\left(\left|{y^{2} - 2}\right| \right)} + \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} 
=
            /     /      2\        \      /|      2|\ 
 -re(c) + I*\- arg\-2 + y / + im(c)/ + log\|-2 + y |/ 
------------------------------------------------------
                        2                            2
/     /      2\        \    /            /|      2|\\ 
\- arg\-2 + y / + im(c)/  + \-re(c) + log\|-2 + y |//
i(im⁡(c)−arg⁡(y2−2))+log⁡(∣y2−2∣)−re⁡(c)(log⁡(∣y2−2∣)−re⁡(c))2+(im⁡(c)−arg⁡(y2−2))2\frac{i \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right) + \log{\left(\left|{y^{2} - 2}\right| \right)} - \operatorname{re}{\left(c\right)}}{\left(\log{\left(\left|{y^{2} - 2}\right| \right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)} - \arg{\left(y^{2} - 2 \right)}\right)^{2}} 
(-re(c) + i*(-arg(-2 + y^2) + im(c)) + log(|-2 + y^2|))/((-arg(-2 + y^2) + im(c))^2 + (-re(c) + log(|-2 + y^2|))^2)
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