Question

How do you use the properties of logarithms to rewrite(contract) each logarithmic expression `2log_2(64) + log_2(2)`?

Answer 1

Use `log_a(a^b) = b` to find:

`2log_2(64)+log_2(2) = 2*6+1 = 13`

Explanation:

`log_a(a^b) = b`, so

`64=2^6` so `log_2(64) = log_2(2^6) = 6`

`2=2^1` so `log_2(2) = log_2(2^1) = 1`

So `2log_2(64)+log_2(2) = 2*6+1 = 13`