# How do you solve log(3x)=log(5)+log(x-4)?

Mar 1, 2016

$x = 10$

#### Explanation:

Using the laws of logs we can simplify the right hand side to :

$\log \left(3 x\right) = \log \left[\left(5\right) \left(x - 4\right)\right]$

$\therefore \log \left(3 x\right) = \log \left(5 x - 20\right)$

Now take the antilog base 10 on both sides to obtain

$3 x = 5 x - 20$

$\therefore x = \frac{20}{2} = 10$