For $x^a = e^2x$. Determine the solutions as a power of$ e$

Question

For $x^a = e^2x$. Determine the solutions as a power of $e$

One obvious solution is $0$ but I fail to find the second solution.

$x^a - e^2x = 0$

$x(x^{a-1} - e^2) = 0$

I am not sure how to find the other solution please help

Answer 1

The other solution comes from

$$x^{a-1}=e^2$$ and taking the power $1/(a-1)$,

$$x=e^{2/(a-1)}.$$

Answer 2

Let $x$=$e^k$ Then, $$\therefore e^{ka}=e^{k+2}$$$$\Rightarrow ka=k+2$$$$\Rightarrow k= \frac{2}{a-1}$$$$\therefore x=e^{\frac {2}{a-1}}$$