7.016. If $\log _{a} 27=b$, then what is $\log _{\sqrt{3}} \sqrt[6]{a}$?
Solution.

$\log _{\sqrt{3}} \sqrt[6]{a}=\frac{1}{6} \cdot 2 \log _{3} a=\frac{1}{3 \log _{a} 3}=\frac{1}{\log _{a} 27}=\frac{1}{b}$.

Answer: $\frac{1}{b}$.