# How do you solve log_2 3 + log_2 7 = log_2 x?

Jun 8, 2018

$x = 21$

#### Explanation:

Use the addition law of logs.

"If logs are being added, then the numbers are being multiplied"

Note that the bases must be the same for this to apply.

${\log}_{a} b + {\log}_{a} c = {\log}_{a} \left(b \times c\right)$

${\log}_{2} 3 + {\log}_{2} 7 = {\log}_{2} \left(3 \times 7\right) = {\log}_{2} 21$

$x = 21$