Pls any one tell this
Q.11. Show that ${\log }_2\left[{\log }_2\left({\log }_{2}16\right)\right]=1$

Dear Student,

Please find the below required solution.

$$\begin{gathered} LHS \\ {\log }_2\left[{\log }_2\right({\log }_{2}16\left)\right] = {\log }_2\left[{\log }_2\right({\log }_2{2}^4\left)\right] \\ = {\log }_2\left[{\log }_2\right(4{\log }_{2}2\left)\right] [\sin ce \log a^m = m\log a] \\ = {\log }_2\left[{\log }_2\right(4\left)\right] [\sin ce {\log }_{a}a = 1] \\ = {\log }_2\left[{\log }_2\right(2^2\left)\right] \\ = {\log }_2\left[2{\log }_2\right(2\left)\right] [\sin ce \log a^m = m\log a] \\ = {\log }_2\left(2\right) [\sin ce {\log }_{a}a = 1] \\ = 1 [\sin ce {\log }_{a}a = 1] \\ RHS [Hence proved] \end{gathered}$$

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