# How do you solve log_7 (x+3) - 2 = log_7 3?

May 11, 2016

$x = \frac{40}{3}$

#### Explanation:

Use log m + log m = log (mn).

Here, ${\log}_{7} \left(x + 3\right) + {\log}_{7} 3 = {\log}_{7} \left(3 \left(x + 3\right)\right) = 2$.

Use that if $c = {\log}_{b} a , a = {b}^{c}$.

Accordingly, $3 \left(x + 3\right) = {7}^{2} = 49$.

So, $x = \frac{40}{3}$.