Question

What is `log_4(2sqrt(2))` ?

Answer 1

`log_4 (2sqrt(2)) = 3/4`

Explanation:

The change of base formula tells us that if `a, b, c > 0` and `a, c != 1` then:

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

Hence:

`log_4 (2sqrt(2)) = log_2 (2sqrt(2)) / log_2 (4) = log_2 (2^(3/2)) / log_2 (2^2) = (3/2) / 2 = 3/4`