Solución detallada
Tenemos la ecuación
$$\log{\left(x \right)} = - \frac{3}{y^{2}}$$
$$\log{\left(x \right)} = - \frac{3}{y^{2}}$$
Es la ecuación de la forma:
log(v)=p
Por definición log
v=e^p
entonces
$$x = e^{\frac{\left(-1\right) 3 \frac{1}{y^{2}}}{1}}$$
simplificamos
$$x = e^{- \frac{3}{y^{2}}}$$
Suma y producto de raíces
[src]
2 2 2 2
3*re (y) 3*im (y) 3*re (y) 3*im (y)
- --------------------------------- + --------------------------------- - --------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2 4 4 2 2 4 4 2 2
/ 6*im(y)*re(y) \ im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) / 6*im(y)*re(y) \
cos|---------------------------------|*e + I*e *sin|---------------------------------|
| 4 4 2 2 | | 4 4 2 2 |
\im (y) + re (y) + 2*im (y)*re (y)/ \im (y) + re (y) + 2*im (y)*re (y)/
$$i e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \sin{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)} + e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \cos{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)}$$
2 2 2 2
3*re (y) 3*im (y) 3*re (y) 3*im (y)
- --------------------------------- + --------------------------------- - --------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2 4 4 2 2 4 4 2 2
/ 6*im(y)*re(y) \ im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) / 6*im(y)*re(y) \
cos|---------------------------------|*e + I*e *sin|---------------------------------|
| 4 4 2 2 | | 4 4 2 2 |
\im (y) + re (y) + 2*im (y)*re (y)/ \im (y) + re (y) + 2*im (y)*re (y)/
$$i e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \sin{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)} + e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \cos{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)}$$
2 2 2 2
3*re (y) 3*im (y) 3*re (y) 3*im (y)
- --------------------------------- + --------------------------------- - --------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2 4 4 2 2 4 4 2 2
/ 6*im(y)*re(y) \ im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) / 6*im(y)*re(y) \
cos|---------------------------------|*e + I*e *sin|---------------------------------|
| 4 4 2 2 | | 4 4 2 2 |
\im (y) + re (y) + 2*im (y)*re (y)/ \im (y) + re (y) + 2*im (y)*re (y)/
$$i e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \sin{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)} + e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \cos{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)}$$
/ 2 2 \
3*\im (y) - re (y)/ 6*I*im(y)*re(y)
--------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2
im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y)
e
$$e^{\frac{3 \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{6 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}}$$
exp(3*(im(y)^2 - re(y)^2)/(im(y)^4 + re(y)^4 + 2*im(y)^2*re(y)^2) + 6*i*im(y)*re(y)/(im(y)^4 + re(y)^4 + 2*im(y)^2*re(y)^2))
2 2 2 2
3*re (y) 3*im (y) 3*re (y) 3*im (y)
- --------------------------------- + --------------------------------- - --------------------------------- + ---------------------------------
4 4 2 2 4 4 2 2 4 4 2 2 4 4 2 2
/ 6*im(y)*re(y) \ im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) im (y) + re (y) + 2*im (y)*re (y) / 6*im(y)*re(y) \
x1 = cos|---------------------------------|*e + I*e *sin|---------------------------------|
| 4 4 2 2 | | 4 4 2 2 |
\im (y) + re (y) + 2*im (y)*re (y)/ \im (y) + re (y) + 2*im (y)*re (y)/
$$x_{1} = i e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \sin{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)} + e^{- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} + \frac{3 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}}} \cos{\left(\frac{6 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4}} \right)}$$
x1 = i*exp(-3*re(y)^2/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4) + 3*im(y)^2/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4))*sin(6*re(y)*im(y)/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4)) + exp(-3*re(y)^2/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4) + 3*im(y)^2/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4))*cos(6*re(y)*im(y)/(re(y)^4 + 2*re(y)^2*im(y)^2 + im(y)^4))