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0.5ln(y)=-ln(x+1) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
log(y)              
------ = -log(x + 1)
  2
log⁡(y)2=−log⁡(x+1)\frac{\log{\left(y \right)}}{2} = - \log{\left(x + 1 \right)}
Simplificar
Solución detallada
Tenemos la ecuación
log⁡(y)2=−log⁡(x+1)\frac{\log{\left(y \right)}}{2} = - \log{\left(x + 1 \right)}
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
log⁡(x+1)=−log⁡(y)2\log{\left(x + 1 \right)} = - \frac{\log{\left(y \right)}}{2}
Es la ecuación de la forma:
log(v)=p

Por definición log
v=e^p

entonces
x+1=e(−1)12log⁡(y)1x + 1 = e^{\frac{\left(-1\right) \frac{1}{2} \log{\left(y \right)}}{1}}
simplificamos
x+1=1yx + 1 = \frac{1}{\sqrt{y}}
x=−1+1yx = -1 + \frac{1}{\sqrt{y}}
Gráfica
Respuesta rápida [src] 
             /atan2(im(y), re(y))\        /atan2(im(y), re(y))\
          cos|-------------------|   I*sin|-------------------|
             \         2         /        \         2         /
x1 = -1 + ------------------------ - --------------------------
               _________________           _________________   
            4 /   2        2            4 /   2        2       
            \/  im (y) + re (y)         \/  im (y) + re (y)
x1=−1−isin⁡(atan2⁡(im⁡(y),re⁡(y))2)(re⁡(y))2+(im⁡(y))24+cos⁡(atan2⁡(im⁡(y),re⁡(y))2)(re⁡(y))2+(im⁡(y))24x_{1} = -1 - \frac{i \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} + \frac{\cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} 
x1 = -1 - i*sin(atan2(im(y, re(y))/2)/(re(y)^2 + im(y)^2)^(1/4) + cos(atan2(im(y), re(y))/2)/(re(y)^2 + im(y)^2)^(1/4))
Suma y producto de raíces [src] 
suma
        /atan2(im(y), re(y))\        /atan2(im(y), re(y))\
     cos|-------------------|   I*sin|-------------------|
        \         2         /        \         2         /
-1 + ------------------------ - --------------------------
          _________________           _________________   
       4 /   2        2            4 /   2        2       
       \/  im (y) + re (y)         \/  im (y) + re (y)
−1−isin⁡(atan2⁡(im⁡(y),re⁡(y))2)(re⁡(y))2+(im⁡(y))24+cos⁡(atan2⁡(im⁡(y),re⁡(y))2)(re⁡(y))2+(im⁡(y))24-1 - \frac{i \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} + \frac{\cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} 
=
        /atan2(im(y), re(y))\        /atan2(im(y), re(y))\
     cos|-------------------|   I*sin|-------------------|
        \         2         /        \         2         /
-1 + ------------------------ - --------------------------
          _________________           _________________   
       4 /   2        2            4 /   2        2       
       \/  im (y) + re (y)         \/  im (y) + re (y)
−1−isin⁡(atan2⁡(im⁡(y),re⁡(y))2)(re⁡(y))2+(im⁡(y))24+cos⁡(atan2⁡(im⁡(y),re⁡(y))2)(re⁡(y))2+(im⁡(y))24-1 - \frac{i \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} + \frac{\cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} 
producto
        /atan2(im(y), re(y))\        /atan2(im(y), re(y))\
     cos|-------------------|   I*sin|-------------------|
        \         2         /        \         2         /
-1 + ------------------------ - --------------------------
          _________________           _________________   
       4 /   2        2            4 /   2        2       
       \/  im (y) + re (y)         \/  im (y) + re (y)
−1−isin⁡(atan2⁡(im⁡(y),re⁡(y))2)(re⁡(y))2+(im⁡(y))24+cos⁡(atan2⁡(im⁡(y),re⁡(y))2)(re⁡(y))2+(im⁡(y))24-1 - \frac{i \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} + \frac{\cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2} \right)}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} 
=
                          -I*atan2(im(y), re(y)) 
     _________________    -----------------------
  4 /   2        2                   2           
- \/  im (y) + re (y)  + e                       
-------------------------------------------------
                  _________________              
               4 /   2        2                  
               \/  im (y) + re (y)
−(re⁡(y))2+(im⁡(y))24+e−iatan2⁡(im⁡(y),re⁡(y))2(re⁡(y))2+(im⁡(y))24\frac{- \sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}} + e^{- \frac{i \operatorname{atan_{2}}{\left(\operatorname{im}{\left(y\right)},\operatorname{re}{\left(y\right)} \right)}}{2}}}{\sqrt[4]{\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}}} 
(-(im(y)^2 + re(y)^2)^(1/4) + exp(-i*atan2(im(y), re(y))/2))/(im(y)^2 + re(y)^2)^(1/4)
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