log base 4 of 8/log base 8 of 16

Question

question is to simplify

can you rewrite it this way?

4^x = 8
---------
8^x = 16

Answer 1

that's a start. Now consider that

4 = 2^2
8 = 2^3

So,

log_4(8) = (1/2)log_2(8) = 3/2
log_8(16) = (1/4)log_2(16) = 4/3

(3/2)/(4/3) = 9/8