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The equation provided in the image is: \[ e^{4-7x} + 11 = 20 \] To solve for \( x \), we'll follow these steps: 1. Subtract 11 from both sides of the equation. \[ e^{4-7x} = 9 \] 2. Take the natural logarithm (ln) of both sides to get rid of the base \( e \). \[ \ln(e^{4-7x}) = \ln(9) \] 3. Use the property of logarithms that \( \ln(e^y) = y \) to simplify the left side. \[ 4 - 7x = \ln(9) \] 4. Subtract 4 from both sides to isolate the term with \( x \). \[ -7x = \ln(9) - 4 \] 5. Finally, divide both sides by -7 to solve for \( x \). \[ x = \frac{\ln(9) - 4}{-7} \] 6. Now you can either leave the answer in terms of natural logarithm or use a calculator to find a numerical value for \( x \). Using a calculator: \[ x \approx \frac{2.1972 - 4}{-7} \] \[ x \approx \frac{-1.8028}{-7} \] \[ x \approx 0.25754 \] So the solution to the equation is \( x \approx 0.25754 \).
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