# How do you solve 3^ { 7x } = 3.3?

Jan 16, 2018

$x = \frac{1}{7} {\log}_{3} 3.3$

#### Explanation:

${3}^{7 x} = 3.3$

Take log to the base 3 of both sides:

${\log}_{3} {3}^{7 x} = {\log}_{3} 3.3$

Use the rules of logs:

$\to 7 x {\log}_{3} 3 = {\log}_{3} 3.3$
$\to 7 x = {\log}_{3} 3.3$
$\therefore x = \frac{1}{7} {\log}_{3} 3.3$