Help please, and explain.
2 answers:
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
Answer: 2x + y
<u>Step-by-step explanation:</u>
logₐ(3) = x
logₐ(5) = y
logₐ(45) = logₐ(3²· 5)
= logₐ(3)² + logₐ(5)
= 2 logₐ(3) + logₐ(5)
= 2 x + y <em>substituted given values (stated above)</em>
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