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. ${\log }_{4\sqrt[3]{4^2}}\left(\frac{1}{1024}\right)$
$=\frac{\log \left(\frac{1}{1024}\right)}{\log 4{\left(4^2\right)}^{1/3}}=\frac{-\log {\left(2\right)}^{10}}{\log 4^{53}}=\frac{-\log {\left(2\right)}^{10}}{\log {\left[{\left(2\right)}^2\right]}^{5/3}}$
$=\frac{-10\log 2}{\frac{10}{3}\log 2}=-3$