Is there a way to find x when x is an exponent? I'm kind of stuck on how to solve the following.
$10^x = 5^9$
Is there a method or a simple trick to find what is x?

That's precisely what logarithms are for. In this case, the logarithm with base 10 (one of the two most common logarithms).
$$10^x=y$$
take the logarithm on both sides:
$$x=\log_{10}y$$
Using the properties of logarithm, your case gives $x=\log_{10}5^9=9\log_{10}5$.
