Answer
Fill the blanks with
$9, 1, 0, -1, 2, 1/2$
Work Step by Step
By definition, $\log_{a}x=y \Leftrightarrow a^{y}=x$
($\log_{a}x$ is the exponent to which the base $a$ must be raised to give $x$.)
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$f(x)=\log_{9}x$ has base 9, so
$f(9)=\log_{9}9$, because $9=9^{1},$ and $\log_{9}(9^{1})=1\Leftrightarrow 9^{1}=9$
$f(1)=0$, because $\log_{9}(1)=0\Leftrightarrow 9^{0}=1$
$f(1/9)=-1$, because $1/9=9^{-1},$ and $\log_{9}(9^{-1})=-1\Leftrightarrow 9^{-1}=1/9$
$f(81)=2$, because $81=9^{2},$ and $\log_{9}(9^{2})=2\Leftrightarrow 9^{2}=81$
$f(3)=1/2$, because $3=\sqrt{9}=9^{1/2},$ and $\log_{9}(9^{1/2})=1/2\Leftrightarrow 9^{1/2}=3$
