The value of ( ( log 2 9 ) 2 ) 1 log 2 ( log 2 9 ) × ( 7 ) 1 log 4 7 is ______ .

Question

The value of $({{(\log_{2} 9)}^{2})}^{\frac{1}{\log_{2} (\log_{2} 9)}} \times {(\sqrt{7})}^{\frac{1}{\log_{4} 7}}$ is ______ .

Smart Achievers · Accepted Answer

(8)

$({{(\log_{2} 9)}^{2})}^{\frac{1}{\log_{2} (\log_{2} 9)}} \times {(\sqrt{7})}^{\frac{1}{\log_{4} 7}}$

$= {(\log_{2} 9)}^{\frac{2}{\log_{2} (\log_{2} 9)}} \cdot {(\sqrt{7})}^{\log_{7} 4}$

$= {(\log_{2} 9)}^{2 \log_{\log_{2} 9} (2)} \cdot 7^{\frac{1}{2} \log_{7} 4}$

$= 4 \cdot 2 = 8$

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