Question

Find the value of ${\log }_2\left(3^{-{\log }_{3}0.25}\right)$.

Answer 1

Now,

${\log }_2\left(3^{-{\log }_{3}0.25}\right)$

$={\log }_2\left(3^{-{\log }_3\frac{1}{4}}\right)$

$={\log }_2\left(3^{{\log }_{3}4}\right)$

$={\log }_{2}4$

$=2{\log }_{2}2$

$=2$