7.20 Find $\log _{\sqrt{3}} \sqrt[6]{a}$, if it is known that $\log _{a} 27=b$.

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7.20 Applying formulas (7.9), (7.8), and again (7.9) sequentially, we get

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

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