Question

The number of roots of the equation $3x^{{\log }_{5}2}+2^{{\log }_{5}x}=64$ is

• A. 2
• B. 4
• C. 1
• D. 0

Answer 1

Answer: (C)

Let ${\log }_{5}x=t\Rightarrow x=5^t$
$3\cdot 5^{t\cdot {\log }_{5}2}+2^t=64$
$\Rightarrow 3\cdot 2^t+2^t=64\Rightarrow 4\cdot 2^t=64$
$\Rightarrow 2^t=16\Rightarrow t=4\Rightarrow {\log }_{5}x=4$
$\Rightarrow x=625$