Question
If \({\log _4}5 = \left( {{{\log }_4}y} \right)\left( {{{\log }_6}\sqrt 5 } \right),\) then y equals
Option: 36
Solution:
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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