# How do you simplify log_2 14 - log_2 7?

May 14, 2016

${\log}_{2} \left(14\right) - {\log}_{2} \left(7\right) = 1$

#### Explanation:

Using the log rule log_x(a) – log_x(b) = log_x(a/b)

Rewrite the equation as:

${\log}_{2} \left(\frac{14}{7}\right)$ = ${\log}_{2} \left(2\right)$

Use the log rule:

${\log}_{x} \left(x\right)$ = 1

Therefore ${\log}_{2} \left(2\right)$ = 1

So ${\log}_{2} \left(14\right) - {\log}_{2} \left(7\right) = 1$