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Q.
The number of roots of the equation $3 x^{\log _5 2}+2^{\log _5 x}=64$ is
Complex Numbers and Quadratic Equations
Solution:
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 $
$\Rightarrow 2^{ t }=16 \Rightarrow t =4 \Rightarrow \log _5 x =4$
$\Rightarrow x =625$