Example Question - exponential equation with natural logarithm

Solving Exponential Equation for x

The equation in the image is: e^(4 - 7x) + 11 = 20 To solve for x, follow these steps: 1. Subtract 11 from both sides to isolate the exponential term: e^(4 - 7x) = 9 2. Take the natural logarithm (ln) of both sides to remove the base e exponent: ln(e^(4 - 7x)) = ln(9) 3. Since ln(e^y) = y for any y, this simplifies to: 4 - 7x = ln(9) 4. Now isolate x by first subtracting 4 from both sides: -7x = ln(9) - 4 5. Finally, divide both sides by -7 to solve for x: x = (ln(9) - 4) / -7 This will give you the numeric value of x. To find the exact value you can use a calculator.