Sr Examen

asin(u)=Const+log(x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
asin(u) = c + log(x)
$$\operatorname{asin}{\left(u \right)} = c + \log{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$\operatorname{asin}{\left(u \right)} = c + \log{\left(x \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \log{\left(x \right)} = c - \operatorname{asin}{\left(u \right)}$$
Devidimos ambás partes de la ecuación por el multiplicador de log =-1
$$\log{\left(x \right)} = - c + \operatorname{asin}{\left(u \right)}$$
Es la ecuación de la forma:
log(v)=p

Por definición log
v=e^p

entonces
$$x = e^{\frac{c - \operatorname{asin}{\left(u \right)}}{-1}}$$
simplificamos
$$x = e^{- c + \operatorname{asin}{\left(u \right)}}$$
Gráfica
Suma y producto de raíces [src]
suma
                           -re(c) + re(asin(u))      -re(c) + re(asin(u))                          
cos(-im(asin(u)) + im(c))*e                     - I*e                    *sin(-im(asin(u)) + im(c))
$$- i e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)} \right)} + e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)} \right)}$$
=
                           -re(c) + re(asin(u))      -re(c) + re(asin(u))                          
cos(-im(asin(u)) + im(c))*e                     - I*e                    *sin(-im(asin(u)) + im(c))
$$- i e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)} \right)} + e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)} \right)}$$
producto
                           -re(c) + re(asin(u))      -re(c) + re(asin(u))                          
cos(-im(asin(u)) + im(c))*e                     - I*e                    *sin(-im(asin(u)) + im(c))
$$- i e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)} \right)} + e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)} \right)}$$
=
 -re(c) + I*(-im(c) + im(asin(u))) + re(asin(u))
e                                               
$$e^{i \left(- \operatorname{im}{\left(c\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)}\right) - \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}}$$
exp(-re(c) + i*(-im(c) + im(asin(u))) + re(asin(u)))
Respuesta rápida [src]
                                -re(c) + re(asin(u))      -re(c) + re(asin(u))                          
x1 = cos(-im(asin(u)) + im(c))*e                     - I*e                    *sin(-im(asin(u)) + im(c))
$$x_{1} = - i e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}} \sin{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)} \right)} + e^{- \operatorname{re}{\left(c\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(u \right)}\right)}} \cos{\left(\operatorname{im}{\left(c\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(u \right)}\right)} \right)}$$
x1 = -i*exp(-re(c) + re(asin(u)))*sin(im(c) - im(asin(u))) + exp(-re(c) + re(asin(u)))*cos(im(c) - im(asin(u)))