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

Dec 12, 2016

$\textcolor{g r e e n}{x = \frac{103}{4}}$

#### Explanation:

It is important to remember the basic relation:

$\textcolor{red}{\text{~~~~~~~~~~~~~~~~~~~~~~~~~~~}}$
$\textcolor{red}{\text{| ")color(blue)(log_b a =c)" means "color(blue)(b^c=a)color(red)(" |}}$
$\textcolor{red}{\text{~~~~~~~~~~~~~~~~~~~~~~~~~~~}}$

(also remember that the default base for $\log$ is $10$)

Therefore
$\textcolor{w h i t e}{\text{XXX}} \log \left(4 x - 3\right) = 2 \Leftrightarrow {\log}_{10} \left(4 x - 3\right) = 2$
means
$\textcolor{w h i t e}{\text{XXX}} {10}^{2} = 4 x - 3$

$\rightarrow 4 x - 3 = 100$

$\rightarrow 4 x = 103$

$\rightarrow x = \frac{103}{4}$