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Nataly_w [17]
3 years ago
15

Help please, and explain.

Mathematics
2 answers:
Sati [7]3 years ago
8 0

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

Korvikt [17]3 years ago
4 0

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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