Solve an equation with $e^{(x-2)}=e^{4}\cdot e^{\sqrt{x}}$ $$e^{(x-2)}=e^{4}e^\sqrt{x}$$
I know that $x = 9$ and I can show the calculations like this:
$$e^{(x-2)} = e^{\sqrt{x}+4}$$
and now I need to get the $x$ to the right side but I dont know how.

Hint: Since the function $f(x)=e^x$ is injective (or one-to-one), we know that $e^a=e^b \implies a=b$. So we may equate exponents to obtain:
$$
x-2=\sqrt{x}+4
$$
