Answer
$-\displaystyle \frac{1}{2}$
Work Step by Step
$\log_{b}x=y $ is equivalent to $ b^{y}=x.\qquad (*)$
Consequently,$\qquad \log_{b}b^{x}=x.\qquad (**)$
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$\displaystyle \frac{1}{\sqrt{3}}=\frac{1}{3^{1/2}}=3^{-1/2}\quad $... (we applied rules for exponents)
$\displaystyle \log_{3}\frac{1}{\sqrt{3}}=\log_{3}3^{-1/2}=\quad $... apply (**)
= $-\displaystyle \frac{1}{2}$
