The value of log 2 ⁡ 9 2 1 log 2 ⁡ log 2 ⁡ 9 × 7 1 log 4 ⁡ 7 is_____.

log 2 ⁡ 9 2 log 2 ⁡ log 2 ⁡ 9 × 7 1 2 log 4 ⁡ 7 = ( log 2 9 ) 2 log ( log 2 9 ) 2 × 7 1 2 log 7 4 = ( log 2 9 ) log ( log 2 9 ) 2 2 × 7 log 7 4 1 2 = 2 2 × 4 1 2 = 4 × 2 = 8

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Mathematics - Basic maths Question with Solution | TestHub

MathematicsBasic mathsLogarithmEasy2 minPYQ_2018

MathematicsEasyinteger

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

Answer:

Solution:

$\log_{2} 9^{\frac{2}{\log_{2} (\log_{2} 9)}} \times 7^{\frac{\frac{1}{2}}{\log_{4} 7}}$
$= {(\log_{2} 9)}^{2 \log_{(\log_{2} 9)} 2} \times 7^{\frac{1}{2} \log_{7} 4}$
$= {(\log_{2} 9)}^{\log_{(\log_{2} 9)} 2^{2}} \times 7^{\log_{7} 4^{\frac{1}{2}}}$
$= 2^{2} \times 4^{\frac{1}{2}}$
$= 4 \times 2 = 8$

Stream:JEE_ADVSubject:MathematicsTopic:Basic mathsSubtopic:Logarithm

⏱ 2mℹ️ Source: PYQ_2018

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