`log_8(32)` Evaluate the logarithm.

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`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))`


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


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)`


Therefore,  `log_8(32)=5/3` .

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