# How do you solve  log_11 (y + 8) + log_11 4 = log_11 60?

Sep 6, 2015

$y = 7$

#### Explanation:

From laws of logs, the log of the sum is the product of the logs.
So left hand side of equation reduces to

${\log}_{11} \left(4 y + 32\right) = {\log}_{11} \left(60\right)$

Now take the anti-log base 11 on both sides to yield:

$4 y + 32 = 60$

This is now a normal linear equation in y which may be solved by normal methods to eventually get $y = 7$.