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Question

Simplify $log \sqrt[4]{729 \sqrt[3]{9^{- 1} . 27^{- \frac{4}{3}}}} .$

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Solution

$log \sqrt[4]{729 \sqrt[3]{9^{- 1} . 27^{- \frac{4}{3}}}}$
$= log \sqrt[4]{729 \sqrt[3]{3^{- 2} . 3^{- 4}}}$
$= log \sqrt[4]{729 \times 3^{- 2}}$
$= log 3$

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