If \log _{4} 5=(\log _{4} y)(\log _{6} \sqrt{5}), then y equals

CAT 2020 Exam Shift 1 Solved Paper

Question : 55 of 76

Marks: +1, -0

\log _{4} 5=(\log _{4} y)(\log _{6} √{5}),

then y equals

Solution:

\log _{4} 5=(\log _{4} y)(\log _{6} √{5})

⇒ \;{\log _{4} 5}/{\log _{6} √{5}}=\log _{4} y

⇒ \log _{4} 5 × \log _{6} √{5}=\log _{4} y

⇒ 2(\log _{4} 5)(\log _{5} 6)=(\log _{4} y)

⇒ 2 \log _{4} 6=\log _{4} y

⇒ \log _{4} 6^{2}=\log _{4} y

⇒ \log _{4} 36=\log _{4} y

⇒ y=36

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