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#