CAT 2018 Slot 1 QA Question & Solution
AlgebraMedium
Question
If x is a positive quantity such that $2^{x}=3^{\log_{5}{2}}$. then x is equal to
Options
$\log_{5}{8}$
$1+\log_{3}({\frac{5}{3}})$
$\log_{5}{9}$
$1+\log_{5}({\frac{3}{5}})$
Solution
Givne that: $2^{x}=3^{\log_{5}{2}}$
$\Rightarrow$ $2^{x}=2^{\log_{5}{3}}$
$\Rightarrow$ $x=\log_{5}{3}$
$\Rightarrow$ $x=\log_{5}{\dfrac{3*5}{5}}$
$\Rightarrow$ $x=\log_{5}{5}+\log_{5}{\dfrac{3}{5}}$
$\Rightarrow$ $x=1+\log_{5}{\dfrac{3}{5}}$. Hence, option D is the correct answer.