I am pretty confuse how to do this

Question

Find $\log_8 27$ when $\log_2 3 = a$.

What is the solution?

Answer 1

$\log_{2}3 = a$ means that $2^a = 3$. By cubing both sides we get

$(2^a)^3 = 3^3$

$\Rightarrow (2^3)^a = 3^3$

$\Rightarrow 8^a = 27$

$\Rightarrow \log_{8}27 = a$