Solving an equation with different bases, each to an unknown power, but with a third value

28 Views Asked by At

This is a relatively straightforward question, but neither myself nor my colleagues are able to come up with a tidy solution without brute force:

Represent $x$ algebraically, given the equation

$$4^{2x-1} = 3^{x+3}+1$$

I have looked around the internet and I cannot seem to find any method to properly solving this problem. It's really the +1 at the end that messes everything up for me. Help!