Exponent to logarithm conversion

Question

So I came across this notation:

cn^(3/2) is Θ(n^(log_4(8))) = Θ(n^(3/2))

here: http://www.cs.cornell.edu/courses/cs3110/2014sp/recitations/24/using-the-substitution-and-master-method.html (under "Examples for the master method")

Why is n^(3/2) == n^(log_4(8)) ?

Answer 1

Because $\log_4(8) = \frac32$.

Note that $$ 4^\frac32 = \left(\sqrt{4}\right)^3 = 2^3 = 8 $$