Question

How to evaluate this logarithmic function?

Answer 1

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`

Answer 2

(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`