Question - Solving Exponential Equation
Solution:
The image shows the following exponential equation:e^(4 - 7x) + 11 = 20To solve the equation for x, we'll follow these steps:1. First, isolate the exponential term:e^(4 - 7x) = 20 - 11e^(4 - 7x) = 92. Next, we would take the natural logarithm (ln) of both sides to get the exponent by itself:ln(e^(4 - 7x)) = ln(9)3. Since ln(e^y) = y for any y (because ln and e are inverse functions), we can simplify the left-hand side:4 - 7x = ln(9)4. Lastly, we'll solve for x:7x = 4 - ln(9)x = (4 - ln(9)) / 7To find the numerical value, compute:ln(9) ≈ 2.1972So,x ≈ (4 - 2.1972) / 7x ≈ 1.8028 / 7x ≈ 0.2575Therefore, the solution to the equation isx ≈ 0.2575.
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