# How do you solve log_ 2 (x+2) - log_2 (x-5) = 3?

Mar 18, 2016

same base so you can add the log terms
log2 (x+2)/(x-5 =3
so now you can convert this to exponent form:
We will have
$\frac{x + 2}{x - 5} = {2}^{3}$
or

$\frac{x + 2}{x - 5} = 8$ which is pretty simple to solve since

x + 2 = 8(x - 5)
7x = 42
x = 6

quick check by substitution to the original equation will confirm solution.