For the equation 3^x=4^ x^2 , the correct statement(s) is/are:

For the equation

3^x=4^{x^2}

, the correct statement(s) is/are:

Options

Anumber of solutions is 2 .
Bnumber of solution is 1 .
Cone of the solution is $\log _4(\sqrt{3 \sqrt{3 \sqrt{3 \ldots \ldots \infty}}})$
Dthe sum of all the solutions is $\log _4 \l$ left((1+\s $sqrt{2})^2-2^{\frac{3}{2}})$

D. the sum of all the solutions is $\log _4 \l$ left((1+\s $sqrt{2})^2-2^{\frac{3}{2}})$

3^x=4^{x^2}

\begin{aligned} & \Rightarrow \quad x \log _2 3=x^2 \log _2 4 \\ & \Rightarrow \quad x=0, x=\frac{1}{2} \log _2 3=\log _4 3\end{aligned}