1. The problem statement, all variables and given/known data ##log _3\left(x-5\right) + log_3\left(x+3\right) = 2## I'm having trouble with applying properties of logarithms to solve equations, I think misunderstanding something fundamental here, I get most of the questions right but there are a handful that I have no idea what I am doing. Please help. 2. Relevant equations 3. The attempt at a solution I try to condense the logs into one with the product rule so: ##log_3\left(x^2-2x-15\right) = 2## then I rewrite it in exponential form: ##3^2=x^2-2x-15## Now I figured that getting rid of the logs would make this quadratic equation manageable but I am coming up nowhere near the right answer (I peaked, its 6). If I add 15 to both sides I get: ##24=x^2-2x## but I don't know what to do with the quadratic...I feel like I messed up trying to get rid of the logs but I cant really identify where I screwed up. I tried to rework it a couple times with different tricks but I still am nowhere close. Any help would be appreciated.