The value of ( ( log 2 9 ) 2 ) 1 log 2 ( log 2 9 ) × ( 7 ) 1 log 4 7 is ________. [2018]

Question

The value of $({{(\log_{2} 9)}^{2})}^{\frac{1}{\log_{2} (\log_{2} 9)}} \times {(\sqrt{7})}^{\frac{1}{\log_{4} 7}}$ is ________. [2018]

Smart Achievers · Accepted Answer

(8)

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

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

$= {(\log_{2} 9)}^{\log_{(\log_{2} 9)} 4} \times 7^{\log_{7} 2} = 4 \times 2 = 8$

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