Solve for \( x: \) \[ \begin{array}{l}5^{x}=41 \\ x=\end{array} \]

To find \( x \) in the equation \( 5^{x} = 41 \), start by taking the logarithm of both sides. You can use either natural logarithm (\(\ln\)) or logarithm base 10 (\(\log\)). Using natural logarithm, we have: \[ x = \frac{\ln(41)}{\ln(5)} \] Now, calculate \( \ln(41) \) and \( \ln(5) \). Approximating these values gives: \(\ln(41) \approx 3.713\) and \(\ln(5) \approx 1.609\). So: \[ x \approx \frac{3.713}{1.609} \approx 2.304 \] Thus, the solution is: \[ x \approx 2.304 \]