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

$$\mathrm{A}={\left({\left({\log }_{2}9\right)}^2\right)}^{\frac{1}{{\log }_2\left({\log }_{2}9\right)}}\times {\left(\sqrt{7}\right)}^{\frac{1}{{\log }_{4}7}}=?$$

Answered by liberty last updated on 25/Jun/21

$$\frac{1}{\log {}_2\left(\log {}_{2}9\right)}=\log {}_{\left(\log {}_{2}9\right)}\left(2\right)$$$$\Rightarrow \mathrm{A}={\left({\left(\log {}_{2}9\right)}^{\log {}_{\left(\log {}_{2}9\right)}\left(2\right)}\right)}^2\times {\left(7^{\log {}_7\left(4\right)}\right)}^{\frac{1}{2}}$$$$\Rightarrow \mathrm{A}=4\times \sqrt{4}=8.$$

Commented by SOMEDAVONG last updated on 25/Jun/21

$$\mathrm{Thanks}\mathrm{sir}!$$

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