pi^x=x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Suma y producto de raíces
[src]
re(W(-log(pi))) I*im(W(-log(pi)))
- --------------- - -----------------
log(pi) log(pi)
$$- \frac{\operatorname{re}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}}$$
re(W(-log(pi))) I*im(W(-log(pi)))
- --------------- - -----------------
log(pi) log(pi)
$$- \frac{\operatorname{re}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}}$$
re(W(-log(pi))) I*im(W(-log(pi)))
- --------------- - -----------------
log(pi) log(pi)
$$- \frac{\operatorname{re}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}}$$
-(I*im(W(-log(pi))) + re(W(-log(pi))))
---------------------------------------
log(pi)
$$- \frac{\operatorname{re}{\left(W\left(- \log{\left(\pi \right)}\right)\right)} + i \operatorname{im}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}}$$
-(i*im(LambertW(-log(pi))) + re(LambertW(-log(pi))))/log(pi)
re(W(-log(pi))) I*im(W(-log(pi)))
x1 = - --------------- - -----------------
log(pi) log(pi)
$$x_{1} = - \frac{\operatorname{re}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}} - \frac{i \operatorname{im}{\left(W\left(- \log{\left(\pi \right)}\right)\right)}}{\log{\left(\pi \right)}}$$
x1 = -re(LambertW(-log(pi)))/log(pi) - i*im(LambertW(-log(pi)))/log(pi)
x1 = 0.195313809384306 - 1.23520114807585*i
x1 = 0.195313809384306 - 1.23520114807585*i