CAT 2020 Quant Question [Slot 1] with Solution 05

Question

If \({\log _4}5 = \left( {{{\log }_4}y} \right)\left( {{{\log }_6}\sqrt 5 } \right),\) then y equals

Option: 36
Solution:

\({\log _4}5 = \left( {{{\log }_4}y} \right)\left( {{{\log }_6}\sqrt 5 } \right)\)

\( \Rightarrow \frac{{{{\log }_4}5}}{{{{\log }_6}\sqrt 5 }} = {\log _4}y\)

\( \Rightarrow {\log _4}5 \times {\log _6}\sqrt 5  = {\log _4}y\)

\( \Rightarrow 2\left( {{{\log }_4}5} \right)\left( {{{\log }_5}6} \right) = \left( {{{\log }_4}y} \right)\)

\( \Rightarrow 2{\log _4}6 = {\log _4}y\)

\( \Rightarrow {\log _4}{6^2} = {\log _4}y\)

\( \Rightarrow {\log _4}36 = {\log _4}y\)

\( \Rightarrow y = 36\)

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