# How do you solve ln(x + 5) - ln(3) = ln(x - 3)?

Jul 8, 2015

I found $x = 7$

#### Explanation:

You can use one rule of the logs:
$\log a - \log b = \log \frac{a}{b}$
to get:
$\ln \left(\frac{x + 5}{3}\right) = \ln \left(x - 3\right)$
take the exponential of both sides:
${e}^{\ln \left(\frac{x + 5}{3}\right)} = {e}^{\ln \left(x - 3\right)}$
that gives you (cancelling $\ln$ and $e$):
$\frac{x + 5}{3} = x - 3$
$x + 5 = 3 x - 9$
$2 x = 14$
$x = 7$