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JEE Advanced 2018Paper 1
Exam
JEE Advanced
Year
2018
Paper
Paper 1
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Advanced 2018 · Paper 1 · Mathematics · Basics of Mathematics

The value of ( ( _ 2 9) ^ 2 ) ^ 1 _ 2 ( _ 2 9) × ( 7 ) ^ 1 _ 4 7...

The value of ((log⁡29)2)1log⁡2(log⁡29)×(7)1log⁡47{\left({\left(\log_{2} 9\right)}^{2}\right)}^{\dfrac{1}{\log_{2} \left(\log_{2} 9\right)}} \times {\left(\sqrt{7}\right)}^{\dfrac{1}{\log_{4} 7}} is_____.

Correct answer

0

Step-by-step solution

log⁡292log⁡2(log⁡29)×712log⁡47\log_{2} {9}^{\dfrac{2}{\log_{2} \left(\log_{2} 9\right)}} \times {7}^{\dfrac{\dfrac{1}{2}}{\log_{4} 7}}
=(log⁡29)2log⁡(log⁡29)2×712log⁡74= {( \log_{2} 9 )}^{2\log_{( \log_{2} 9 )} 2} \times {7}^{\dfrac{1}{2} \log_{7} 4}
=(log⁡29)log⁡(log⁡29)22×7log⁡7412= {( \log_{2} 9 )}^{\log_{( \log_{2} 9 )} {2}^{2}} \times {7}^{\log_{7} {4}^{\dfrac{1}{2}}}
=22×412= {2}^{2} \times {4}^{\dfrac{1}{2}}
=4×2=8= 4 \times 2 = 8
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