Question:
If x is a positive quantity such that \({2^x} = {3^{{{\log }_5}2}}\) , then x is equal to
- \(1 + {\log _3}\frac{5}{3}\)
- \({\log _5}8\)
- \(1 + {\log _5}\frac{3}{5}\)
- \({\log _5}9\)
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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