# How do you solve log_3 y – log_3 7 = log_3 2?

Jun 25, 2015

Subtracting logs is dividing the arguments

#### Explanation:

${\log}_{3} y - {\log}_{3} 7 = {\log}_{3} \left(\frac{y}{7}\right) \to$
${\log}_{3} \left(\frac{y}{7}\right) = {\log}_{3} 2 \to$
$\frac{y}{7} = 2 \to y = 14$

This will work with all logs, as long as all suffixes are the same.