if f(x)= log,2(x) and g(x)=log ,4(x) then find f(g(2))

Question

The commas are indicating the sub numbers instead of the regular log 10

Answer 1

g(x) = log₄(x)

g(2) = log₄(2)

g(2) = log₄(4^1/2) [4^1/2 = √4 = 2]

g(2) = (1/2) log₄(4) [Log property: log(a^b) = b log(a)]

g(2) = 1/2 [log₄(4) = 1]

f(g(2)) = f(1/2) = log₂(1/2) = log₂(2^-1) = ____? [Use log(a^b) = b log(a) and log_a(a) = 1]