log_1/2 1/4root2 = ???
 

Please find below the solution to the asked query:

We have : ${\log }_2 \frac{1}{4\sqrt{2}}$ , So

$$\begin{gathered} \Rightarrow {\log }_2\left( \frac{1}{2^2 \times 2^{{\displaystyle \frac{1}{2}}}} \right) \\ \Rightarrow lo{g}_2\left( \frac{1}{2^{{\displaystyle 2 + \frac{1}{2}}}} \right) \\ \Rightarrow lo{g}_2\left( \frac{1}{2^{{\displaystyle \frac{5}{2}}}} \right) \\ \Rightarrow {\log }_2\left( 2^{- \frac{5}{2}} \right) \\ \Rightarrow - \frac{5}{2} \times {\log }_2\left( 2\right) ( \mathrm{We} \mathrm{know} {\log }_{\mathrm{e}}{\mathrm{a}}^{\mathrm{b}} =\mathrm{b} {\log }_{\mathrm{e}}\mathrm{a} ) \\ \Rightarrow - \frac{5}{2} \times 1 ( \mathrm{We} \mathrm{know} {\log }_{\mathrm{a}}\mathrm{a} = 1 ) \\ \mathbf{\Rightarrow }\mathbf{-}\mathbf{ }\mathbf{ }\frac{\mathbf{5}}{\mathbf{2}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$

Hope this information will clear your doubts about topic.