Explanation

If4^a=8^b, find the ratio $frac{a}{b}$

Write both sides with base 2:

$$4^a = (2^2)^a = 2^{2a} \ 8^b = (2^3)^b = 2^{3b} Rightarrow 2^{2a} = 2^{3b} Rightarrow 2a = 3b Rightarrow frac{a}{b} = frac{3}{2}$$

⇒2^2a=2^3b⇒2a=3b⇒a​/b=3/2​