# How do you solve Log (x + 3) - Log (2x - 1) = Log 4?

Jan 7, 2016

x = 1

#### Explanation:

on the left hand side of the equation we make use of the following law of logs :

$\log x - \log y = \log \left(\frac{x}{y}\right)$

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

$\Rightarrow \log \left(\frac{x + 3}{2 x - 1}\right) = \log 4$

$\Rightarrow \frac{x + 3}{2 x - 1} = 4$

and so 4 ( 2x - 1 ) = x + 3

$\Rightarrow 8 x - 4 = x + 3$

$\Rightarrow 7 x = 7$

$\Rightarrow x = 1$