Solve \( 3^{x}=42 \). Round to the nearest hundredth.

To solve \( 3^{x} = 42 \), we can take the logarithm of both sides. Using the natural logarithm (though common logarithm can also be used), we have: \[ \ln(3^{x}) = \ln(42) \] Using the logarithmic identity \( \ln(a^b) = b \cdot \ln(a) \), we rewrite this as: \[ x \cdot \ln(3) = \ln(42) \] Now, we can isolate \( x \): \[ x = \frac{\ln(42)}{\ln(3)} \] Now, we calculate the values: \[ \ln(42) \approx 3.7612 \quad \text{and} \quad \ln(3) \approx 1.0986 \] So, \[ x \approx \frac{3.7612}{1.0986} \approx 3.42 \] Rounding to the nearest hundredth, the solution is: \[ x \approx 3.42 \]