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CAT 2018 [SLOT 1] Quant Question with Solution 12

If x is a positive quantity such that \({2^x} = {3^{{{\log }_5}2}}\) , then x is equal to

  1. \(1 + {\log _3}\frac{5}{3}\)
  2. \({\log _5}8\)
  3. \(1 + {\log _5}\frac{3}{5}\)
  4. \({\log _5}9\)
Show Answer
Correct Answer: 3

Givne that: $2^{x}=3^{\log_{5}{2}}$

$\Rightarrow$ $2^{x}=2^{\log_{5}{3}}$

$\Rightarrow$ $x=\log_{5}{3}$

$\Rightarrow$ $x=\log_{5}{\frac{3*5}{5}}$

$\Rightarrow$ $x=\log_{5}{5}+\log_{5}{\frac{3}{5}}$

$\Rightarrow$ $x=1+\log_{5}{\frac{3}{5}}$.

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