Answer
$a.\qquad 3$
$b.\displaystyle \qquad \frac{1}{2}$
$c.\displaystyle \qquad \frac{1}{4}$
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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What follows from the definition is that
$\log_{a}(a^{x})=x$
a.
$\log_{5}125=\log_{5}5^{3}=3\qquad $(because $5^{3}=125$)
b.
$\displaystyle \log_{49}7=\log_{5}49^{1/2}=\frac{1}{2}\qquad $(because $7^{2}=49, 49^{1/2}=7$)
c.
$\displaystyle \log_{9}\sqrt{3}=\log_{9}\sqrt{9^{1/2}}=\log_{9}(9^{1/2})^{1/2}=\log_{9}9^{1/4}=\frac{1}{4}\qquad $
(because $3^{2}=9, 9^{1/2}=3$)
