Question

How do you evaluate `log_4 32`?

Answer 1

Use the change of base formula to get:

`log_4 32 = (log_2 2^5) / (log_2 2^2) = 5/2`

Explanation:

In general, `log_a b = (log_c b) / (log_c a)`

`32 = 2^5` and `4 = 2^2`

So `log_2(32) = log_2(2^5) = 5`

and `log_2(4) = log_2(2^2) = 2`

Hence `log_4(32) = 5/2`