How do you show that this statement is true $log_5 25=2log_5 5$ ?

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Answer 1 · 2016-11-26T21:32:08

Using log $a^m -= mlog a$ (any log base):

$log_5 25 = log_5 5^2$
$:. log_5 25 = (2)log_5 5$
$:. log_5 25 = 2log_5 5$ QED

NB: $log_a a = 1$ so we can also write

$log_5 25 = (2)(1)$
$:. log_5 25 = 2$

How do you show that this statement is true log_5 25=2log_5 5log_5 25=2log_5 5?