Question

If $3x^{{\log }_{5}2}+2^{{\log }_{5}x}=64$ then $x$ is equal to

• A. $625$
• B. $250$
• C. $125$
• D. None of these

Answer 1

The correct option is A $625$

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

$\Rightarrow 3\times 2^{{\log }_{5}x}+2^{{\log }_{5}x}=64$ using

$a^{{\log }_{b}c}=c^{{\log }_{b}a}$

$\Rightarrow 4\times 2^{{\log }_{5}x}=64$

$\Rightarrow 2^2\times 2^{{\log }_{5}x}=2^6$

$\Rightarrow 2+{\log }_{5}x=6$ .................... taking log on both sides

$\Rightarrow {\log }_{5}x=6-2=4$

$\Rightarrow x=5^4=625$