Step-by-step explanation:
Here we make use of the laws of logarithms:
log_a(PQ) = log_a(P)+log_a(Q)
which implies the following corollary
log_a(P^2) = log_a(P)+log_a(P) = 2log_a(P)
Notice how the log of a product is reduced to the sum of the log of the factors. (Advantage is taken of this fact in the use of logarithm tables before the wide-spread use of electronic calculators (pre-70's) )
So substituting
x=log_a(3)
y=log_a(5)
we have
log_a(45) = log_a(3^2 * 5) = log_a(3^2) + log_a(5)=2log_a(3)+log_a(5)
=2x+y
