log 4 4 2 3 ( 1 1024 ) =

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Solution

Q.
$\log_{4 \sqrt[3]{4^{2}}} (\frac{1}{1024}) =$

1 - 3

2 3

3 - 5

4 5

Ans.
(1)

$We have,$ $\log_{4 \sqrt[3]{4^{2}}} (\frac{1}{1024})$

$= \frac{\log (\frac{1}{1024})}{\log (4 (4^{2})^{1 / 3})} = \frac{- \log {(2)}^{10}}{\log 4^{5 / 3}}$

$= \frac{- \log {(2)}^{10}}{\log {[(2)^{2}]}^{5 / 3}} = \frac{- 10 \log 2}{\frac{10}{3} \log 2} = - 3$

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