# How do you solve log(2x-8)=4?

Mar 31, 2018

$x = \frac{{e}^{4} + 8}{2} \approx 31.3$

#### Explanation:

(Assuming log base e)

The trick is to rewrite 4 as a logarithm so that the logarithms can be removed. $4 = \log \left({e}^{4}\right)$

$\log \left(2 x - 8\right) = 4$

$\log \left(2 x - 8\right) = \log \left({e}^{4}\right)$
$2 x - 8 = {e}^{4}$

$2 x = {e}^{4} + 8$

$x = \frac{{e}^{4} + 8}{2} \approx 31.3$