Question

The number of real values of $x,$ satisfying $3^{2{\log }_{3}x}-2x-3=0$ is

• A. $0$
• B. $1$
• C. $2$
• D. more than $2$

Answer 1

The correct option is B $1$

$3^{2{\log }_{3}x}-2x-3=0$
For the $\log$ to be defined,
$x>0\cdots \left(1\right)$

Now, $3^{{\log }_3{x}^2}-2x-3=0$
$\Rightarrow x^2-2x-3=0(\because a^{{\log }_{a}b}=b)\Rightarrow (x-3)(x+1)=0\therefore x=3(\because x>0)$

Hence, there is only one solution of the given equation.