# How do you solve the equation log(3+x)-log(x-5)=log(2)?

Feb 9, 2018

$x = 13$

#### Explanation:

Use the logarithm property that:

$\log a - \log b = \log \left(\frac{a}{b}\right)$

Therefore, we can solve this equation like this:

$\log \left(3 + x\right) - \log \left(x - 5\right) = \log \left(2\right)$

$\log \left(\frac{3 + x}{x - 5}\right) = \log \left(2\right)$

$\frac{3 + x}{x - 5} = 2$

$3 + x = 2 \left(x - 5\right)$

$3 + x = 2 x - 10$

$3 = x - 10$

$13 = x$