`log_8(32)` Evaluate the logarithm.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`log_8 (32)`

To evaluate, factor 32.

`=log_8 (2^5)`

Then, apply the formula of change base `log_b(a) = (log_c(a))/(log_c(b))` .

`= (log_2 (2^5))/(log_2 (8))`

`=(log_2(2^5))/(log_2(2^3))`

Also, apply the rule `log_b (a^m) = m*log_b (a)` .

`=(5*log_2(2))/(3*log_2(2))`

Take note that when the base and argument of the logarithm are the same, it simplifies to 1, `log_b(b)=1` .

`= (5*1)/(3*1)`

`=5/3`

Therefore,  `log_8(32)=5/3` .

Approved by eNotes Editorial Team