How to evaluate this logarithmic function?

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2 Answers
Apr 26, 2018

B

Explanation:

We use the following rules to find the answer:

a^(m-n)=a^m/a^n

a^(log_a b)=b

So

3^(2-log_3 4)=3^2/3^(log_3 4)=9/4

Apr 26, 2018

(B) 9/4

Explanation:

Remember that in general color(red)(p^(q-r))=p^q * p^(-r)color(red)(=(p^q)/(p^r))
and
that log_v w = x means v^x=w
so color(blue)(v^(log_v w)) is simply v^x where v^xcolor(blue)(=w)

Therefore
color(white)("XXX")color(red)(3^(2-log_3 4))

color(white)("XXX")color(red)(=(3^2)/(3^(log_3 4)))

color(white)("XXX")=(3^2)/color(blue)(3^(log_3 4))

color(white)("XXX")=9/color(blue)4