Please help me with this problem. I've tried at least 6 different methods to solve it and they've ALL been wrong. I'm wasting too much time on this problem.

Here it is:

log5(x+1) - log4(x-2) = 1

Where log5 and log4 are log base 5 and log base 4, respectively. I have tried converting to base 4, tried converting to base 5, and neither has worked. If you can, please take me through it step by step.

According to my book, the answer is supposed to be x = 2.79, and I haven't gotten close to it yet.

Please help me with this problem, I've spent HOURS on it and I'm normally very good with logs and exponents...I REALLY want to get this right in case I see it on an exam. this can't be that complicated so what the hell am I doing wrong? I can't believe I'm having this much trouble with such a simple problem