Question

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

Answer 1

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`