Question

How do you calculate `log_16 512`?

Answer 1

`log_(16) 512 = 9/4`

Explanation:

The change of base formula tells us that if `a, b, c > 0` then:

`log_a b = (log_c b)/(log_c a)`

Note that

`16 = 2^4`

`512 = 2^9`

So we find:

`log_(16) 512 = (log_2 512)/(log_2 16) = (log_2 2^9)/(log_2 2^4) = 9/4`