Solve for \( x: \) \( 5^{x}=32 \) \( x=\square \) You may enter the exact value or round to 4 decimal places.

To solve the equation \( 5^{x} = 32 \), we can take the logarithm of both sides: \[ \log(5^x) = \log(32) \] Using the power rule of logarithms, we get: \[ x \cdot \log(5) = \log(32) \] Now, isolate \( x \): \[ x = \frac{\log(32)}{\log(5)} \] Using a calculator, we can find: \(\log(32) \approx 1.5051\) and \(\log(5) \approx 0.6990\). Now, substitute these values back into the equation: \[ x \approx \frac{1.5051}{0.6990} \approx 2.15 \] So, rounded to four decimal places: \[ x \approx 2.1501 \]