- #1

Illuvitar

- 42

- 1

## Homework Statement

##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.

## Homework Equations

## 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 can't 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.