# How do you solve log_516 - log_5 2t = log_5 2?

Jun 18, 2015

The answer is $t = 4$
I assume that the question should be ${\log}_{5} 16 - {\log}_{5} 2 t = {\log}_{5} 2$

#### Explanation:

First you have to simplify the left side and write the difference of logarythms as a logarythm of a division:

${\log}_{5} \left(\frac{16}{2 t}\right) = {\log}_{5} 2$

Now, when you have just logarythms on both sides and they both have the same base (5) you can get rid of logarythms and write:

$\frac{16}{2 t} = 2$

$\frac{8}{t} = 2$

$8 = 2 t$
$t = 4$