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lnx=-3/y^2 la ecuación

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v

Solución numérica:

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Solución

Ha introducido [src] 
         -3 
log(x) = ---
           2
          y
log⁡(x)=−3y2\log{\left(x \right)} = - \frac{3}{y^{2}}
Simplificar
Solución detallada
Tenemos la ecuación
log⁡(x)=−3y2\log{\left(x \right)} = - \frac{3}{y^{2}}
log⁡(x)=−3y2\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(−1)31y21x = e^{\frac{\left(-1\right) 3 \frac{1}{y^{2}}}{1}}
simplificamos
x=e−3y2x = e^{- \frac{3}{y^{2}}}
Gráfica
Suma y producto de raíces [src] 
suma
                                                           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)/
ie−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))4sin⁡(6re⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4)+e−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))4cos⁡(6re⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4)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)/
ie−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))4sin⁡(6re⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4)+e−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))4cos⁡(6re⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4)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)} 
producto
                                                           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)/
ie−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))4sin⁡(6re⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4)+e−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))4cos⁡(6re⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4)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
e3(−(re⁡(y))2+(im⁡(y))2)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4+6ire⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4e^{\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))
Respuesta rápida [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)          \
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)/
x1=ie−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))4sin⁡(6re⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4)+e−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))4cos⁡(6re⁡(y)im⁡(y)(re⁡(y))4+2(re⁡(y))2(im⁡(y))2+(im⁡(y))4)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))
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