Fill in the Blank 1 point \( e^{9-7 x}+4=81 \) Note: Enter negatives when necessary with no space between the negative sign and the number. Enter your answer as a decimal. If the answer is less than 1, be sure to include a 0 before the decimal.

To solve the equation \( e^{9-7x} + 4 = 81 \), we first isolate the exponential term: 1. Subtract 4 from both sides: \[ e^{9-7x} = 77 \] 2. Take the natural logarithm of both sides: \[ 9 - 7x = \ln(77) \] 3. Solve for \( x \): \[ -7x = \ln(77) - 9 \] \[ x = \frac{9 - \ln(77)}{7} \] Using a calculator, we find \( \ln(77) \approx 4.3438 \). Plugging this value in: \[ x = \frac{9 - 4.3438}{7} \approx \frac{4.6562}{7} \approx 0.6654 \] Thus, the answer is approximately \( 0.6654 \).