# How do you solve ln(x+2) - ln(x-2) = ln3?

Sep 23, 2016

$x = 4$, is the Soln.

#### Explanation:

$\ln \left(x + 2\right) - \ln \left(x - 2\right) = \ln 3$

Since, $\ln a - \ln b = \ln \left(\frac{a}{b}\right)$, we have,

$\ln \left(\frac{x + 2}{x - 2}\right) = \ln 3$

We know that, $\ln$ is $1 - 1$ function, so, we get,

$\frac{x + 2}{x - 2} = 3$.

By Compodando-Dividando,

$\frac{\left(x + 2\right) + \left(x - 2\right)}{\left(x + 2\right) - \left(x - 2\right)} = \frac{3 + 1}{3 - 1}$

$\therefore \frac{2 x}{4} = \frac{x}{2} = \frac{4}{2} = 2$

$\therefore x = 4$

We see that this root satisfy the given eqn.hence,

$x = 4$, is the Soln.