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

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