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

Mar 18, 2018

$\log 2 + \log \left(4 x - 1\right) = 3$

Or, log(2×(4x-1))=3log10=log 10^3

Or, $8 x - 2 = 1000$

So, $8 x = 1002$

Or, $x = 125.25$

Mar 18, 2018

$x = 125.25$

#### Explanation:

the logs can be combined using the rule:
$\log a + \log b = \log a b$
so

$\log \left(2 \left(4 x - 1\right)\right) = 3$
$\log \left(8 x - 2\right) = 3$

to get rid of the log, we put both sides to the power of ten
${10}^{\log \left(8 x - 2\right)} = {10}^{3}$

the ten and the log cancel out, leaving
$8 x - 2 = 1000$
$8 x = 1002$
$x = 125.25$