We have been working with logs and didn't get any examples on how to do these types of problems. I was just wondering if someone could help me out on one of them.
5^(x-1)=2^x
Ouch! So you're needing help with understanding the topic first....
To learn, in general, how to solve this sort of equation, try here. Once you've studied that, the worked solution in the previous reply should make perfect sense!