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

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Answer 1 · 2015-06-18T21:26:03

The answer is $t=4$
I assume that the question should be $log_5 16-log_5 2t=log_5 2$

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

$log_5 (16/(2t))=log_5 2$

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:

$16/(2t)=2$

$8/t=2$

$8=2t$
$t=4$

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