A-log-2-9-2-1-log-2-log-2-9-7-1-log-4-7-

Question Number 144387 by SOMEDAVONG last updated on 25/Jun/21

A = {({(\log_{2} 9)}^{2})}^{\frac{1}{\log_{2} (\log_{2} 9)}} \times {(\sqrt{7})}^{\frac{1}{\log_{4} 7}} = ?

Answered by liberty last updated on 25/Jun/21

\frac{1}{\log_{2} (\log_{2} 9)} = \log_{(\log_{2} 9)} (2)

\Rightarrow A = {({(\log_{2} 9)}^{\log_{(\log_{2} 9)} (2)})}^{2} \times {(7^{\log_{7} (4)})}^{\frac{1}{2}}

\Rightarrow A = 4 \times \sqrt{4} = 8 .

Commented by SOMEDAVONG last updated on 25/Jun/21

Thanks sir!