Question

Find the value of
$\tt( log_{2}(9)^{2} )^{ \frac{1}{ log_{2} log_{2}(9) } } \times ( \sqrt{7} )^{ \frac{1}{ log_{4}(7) } }$
​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\displaystyle\{log_{2}(9)^{2}\}^{\dfrac{1}{log_{2}log_{2}(9)}}\,\times\{\sqrt{7}\}^{\dfrac{1}{log_{4}(7)}}}$

$\tt{=\displaystyle\{log_{2}(81)\}^{log_{log_{2}(9)}(2)}\,\times\{\sqrt{7}\}^{log_{7}(4)}}$

$\tt{=\displaystyle\{log_{2}(81)\}^{log_{log_{2}(\sqrt{81})}(2)}\,\times\{7\}^{\frac{1}{2}log_{7}(4)}}$

$\tt{=\displaystyle\{log_{2}(81)\}^{log_{\frac{1}{2} log_{2}(81)}(2)}\,\times\{7\}^{log_{7}(\sqrt{4})}}$

$\tt{=\displaystyle\{log_{2}(81)\}^{2\,log_{ log_{2}(81)}(2)}\,\times\{7\}^{log_{7}(\sqrt{4})}}$

$\tt{=\displaystyle\{log_{2}(81)\}^{log_{ log_{2}(81)}(2^{2})}\,\times\{7\}^{log_{7}(\sqrt{4})}}$

$\tt{=\displaystyle\{log_{2}(81)\}^{log_{ log_{2}(81)}(4)}\,\times\{7\}^{log_{7}(2)}}$

$\tt{=4\times2}$

$\tt{=8}$

Answer 2

Answer:

Extremely glad that you too carry our program of the daily riddle. I'll strive to reply to yours. Thanks for your support & answers :D