Question

$\log _{4 \sqrt[3]{4^{2}}} \left(\frac{1}{1024}\right) = $

• A. -3
• B. 3
• C. -5
• D. 5

Answer 1

Answer: (A)

We have. $\log _{4 \sqrt[3]{4^{2}}} \left(\frac{1}{1024}\right)$
$ = \frac{\log \left(\frac{1}{1024}\right)}{\log 4\left(4^{2}\right)^{1/ 3}} = \frac{-\log \left(2\right)^{10}}{\log 4^{5 3}} = \frac{- \log \left(2\right)^{10}}{\log \left[\left(2\right)^{2}\right]^{5 / 3 }}$
$ = \frac{-10 \log 2}{\frac{10}{3} \log 2} = -3$