# Math Help - (log) solve for x

1. ## (log) solve for x

log3(x - 5) + log3(x + 3) = 2

i need to solve for x. I know you can use the logx + logy = log(xy) but i can't get any further. help?

2. $log_3(x-5) + log_3(x+3) = log_3((x-5)(x+3)) = 2 = log_3(3^2)$

I used the fact that $log_x(a) + log_x(b) = log_x(ab)$ and that $log_x(x) = 1$ and $log_k(x^n) = n \cdot log_k(x)$

3. Originally Posted by snypeshow
log3(x - 5) + log3(x + 3) = 2

i need to solve for x. I know you can use the logx + logy = log(xy) but i can't get any further. help?
First step: Determine the domain of this equation:

$x-5>0~\wedge~x+3>0~\implies~\boxed{x>5}$

And now proceed as Defunkt has described.