Select the correct answer.What is the solution to this equation?32⁢𝑥=13 A. 1 B. -1 C. -12 D. 12

To solve the equation $3^2x = 13$, we need to isolate $x$. Here are the steps:

1. Rewrite the equation: $3^{2x} = 13$

2. Take the natural logarithm (ln) of both sides: $\ln(3^{2x}) = \ln(13)$

3. Use the logarithm power rule $\ln(a^b) = b \ln(a)$: $2x \ln(3) = \ln(13)$

4. Solve for $x$: $x = \frac{\ln(13)}{2 \ln(3)}$

5. Calculate the value: $x \approx \frac{2.5649}{2 \times 1.0986}$ $x \approx \frac{2.5649}{2.1972}$ $x \approx 1.167$

Since none of the provided options (A. 1, B. -1, C. -12, D. 12) exactly match the calculated value, it appears there might be a mistake in the problem statement or the provided options. However, based on the closest approximation, the answer would be closest to:

A. 1