Question

Solve the equation
${3x}^{{\log }_{5}2}+2^{{\log }_{5}x}=64$

Answer 1

${3x}^{{\log }_{5}2}+2^{{\log }_{5}x}=64$
$\Rightarrow 32^{{\log }_{5}x}+2^{{\log }_{5}x}=42^{{\log }_{5}x}=64$
$\Rightarrow 2^{{\log }_{5}x}=16=2^4$
$\Rightarrow x=625$
Ans: 625