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# 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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