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log(y+1)=c+log(x^2-1)/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                    / 2    \
                 log\x  - 1/
log(y + 1) = c + -----------
                      2
log⁡(y+1)=c+log⁡(x2−1)2\log{\left(y + 1 \right)} = c + \frac{\log{\left(x^{2} - 1 \right)}}{2}
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Gráfica
Suma y producto de raíces [src] 
suma
      _________________________________________________                                                                _________________________________________________                                                              _________________________________________________                                                                _________________________________________________                                                       
     /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\        /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\      /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\        /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\
  4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|     4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|   4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|     4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|
- \/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *cos|-------------------------------------------------| - I*\/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *sin|-------------------------------------------------| + \/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *cos|-------------------------------------------------| + I*\/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *sin|-------------------------------------------------|
                                                           \                        2                        /                                                              \                        2                        /                                                            \                        2                        /                                                              \                        2                        /
(−i(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24sin⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2)−(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24cos⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2))+(i(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24sin⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2)+(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24cos⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2))\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}\right) 
=
0
00 
producto
/      _________________________________________________                                                                _________________________________________________                                                       \ /    _________________________________________________                                                                _________________________________________________                                                       \
|     /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\        /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\| |   /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\        /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\|
|  4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|     4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|| |4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|     4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //||
|- \/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *cos|-------------------------------------------------| - I*\/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *sin|-------------------------------------------------||*|\/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *cos|-------------------------------------------------| + I*\/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *sin|-------------------------------------------------||
\                                                           \                        2                        /                                                              \                        2                        // \                                                         \                        2                        /                                                              \                        2                        //
(−i(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24sin⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2)−(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24cos⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2))(i(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24sin⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2)+(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24cos⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2))\left(- i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)}\right) 
=
     _________________________________________________                                                     
    /                         2                                /  /       2  -2*c\        /       2  -2*c\\
   /  /      /       2  -2*c\\      2/       2  -2*c\   I*atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //
-\/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *e
−(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))2eiatan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)- \sqrt{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}} 
-sqrt((1 + re((1 + y)^2*exp(-2*c)))^2 + im((1 + y)^2*exp(-2*c))^2)*exp(i*atan2(im((1 + y)^2*exp(-2*c)), 1 + re((1 + y)^2*exp(-2*c))))
Respuesta rápida [src] 
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          /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\        /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\
       4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|     4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|
x1 = - \/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *cos|-------------------------------------------------| - I*\/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *sin|-------------------------------------------------|
                                                                \                        2                        /                                                              \                        2                        /
x1=−i(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24sin⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2)−(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24cos⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2)x_{1} = - i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} 
         _________________________________________________                                                                _________________________________________________                                                       
        /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\        /                         2                           /     /  /       2  -2*c\        /       2  -2*c\\\
     4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|     4 /  /      /       2  -2*c\\      2/       2  -2*c\     |atan2\im\(1 + y) *e    /, 1 + re\(1 + y) *e    //|
x2 = \/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *cos|-------------------------------------------------| + I*\/   \1 + re\(1 + y) *e    //  + im \(1 + y) *e    / *sin|-------------------------------------------------|
                                                              \                        2                        /                                                              \                        2                        /
x2=i(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24sin⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2)+(re⁡((y+1)2e−2c)+1)2+(im⁡((y+1)2e−2c))24cos⁡(atan2⁡(im⁡((y+1)2e−2c),re⁡((y+1)2e−2c)+1)2)x_{2} = i \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)},\operatorname{re}{\left(\left(y + 1\right)^{2} e^{- 2 c}\right)} + 1 \right)}}{2} \right)} 
x2 = i*((re((y + 1)^2*exp(-2*c)) + 1)^2 + im((y + 1)^2*exp(-2*c))^2)^(1/4)*sin(atan2(im((y + 1)^2*exp(-2*c), re((y + 1)^2*exp(-2*c)) + 1)/2) + ((re((y + 1)^2*exp(-2*c)) + 1)^2 + im((y + 1)^2*exp(-2*c))^2)^(1/4)*cos(atan2(im((y + 1)^2*exp(-2*c)), re((y + 1)^2*exp(-2*c)) + 1)/2))
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