Logarithms Practice Test 2

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Question : 24 of 39

Marks: +1, -0

If

\log_10a = p

and

\log_10b = q

, then what is

\log_10(a^p b^q )

equal to?

$p^2 + q^2$
$p^2- q^2$
$p^2 q^2$
$p^2/ q^2$

Solution:

\log_10 a=p,\log_10b=q

We have

\log_10a+\log_10b=\log_10(ab)

Now value of

\log_10(a^p-b^q)

=\log_10a^p+\log_10b^q

=p\log_10a+q\log_10b

=p(p)+q(q)=p^2+q^2

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