Question

If ${2.x}^{{\log }_{4}3}+3^{{\log }_{4}x}=27$, then the value of $\sqrt{x}$ will be

Answer 1

The domain of the admissible values of the equation is $x>0$.
The given equation is equivalent to
${2\cdot 3}^{{\log }_{4}x}+3^{{\log }_{4}x}=27$
$\Rightarrow {3\cdot 3}^{{\log }_{4}x}=27$
$\Rightarrow 3^{{\log }_{4}x}=9$
$\Rightarrow 3^{{\log }_{4}x}=3^2$
$\Rightarrow {\log }_{4}x=2$
$\Rightarrow x=4^2=16$
The value of $\sqrt{x}=4$