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

To solve for \( x \) in the equation \( 5^{x} = 41 \), we start by taking the logarithm of both sides. Using the natural logarithm (ln), we can rewrite the equation as: \[ \ln(5^{x}) = \ln(41) \] By using the property of logarithms that states \( \ln(a^b) = b \cdot \ln(a) \), we get: \[ x \cdot \ln(5) = \ln(41) \] Now, we isolate \( x \) by dividing both sides by \( \ln(5) \): \[ x = \frac{\ln(41)}{\ln(5)} \] Now we can calculate \( \ln(41) \) and \( \ln(5) \) using a calculator: - \( \ln(41) \approx 3.713 \) - \( \ln(5) \approx 1.609 \) Now, plugging these values into our equation gives us: \[ x \approx \frac{3.713}{1.609} \approx 2.303 \] So the solution for \( x \) is approximately: \[ x \approx 2.303 \]