Solve for \( x \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{-6 x}=2 \]

To solve the equation \( e^{-6x} = 2 \), we first take the natural logarithm (ln) of both sides: \[ \ln(e^{-6x}) = \ln(2) \] Using the property of logarithms that states \( \ln(e^y) = y \), we can simplify the left side: \[ -6x = \ln(2) \] Now, we solve for \( x \) by dividing both sides by -6: \[ x = -\frac{\ln(2)}{6} \] Next, we compute \( \ln(2) \) approximately, which is \( \ln(2) \approx 0.693147 \). Now substituting this value: \[ x \approx -\frac{0.693147}{6} \approx -0.1155245 \] Rounding this result to the nearest hundredth, we get: \[ x \approx -0.12 \] Thus, the final answer is: \[ x \approx -0.12 \]