Question - Solving Exponential Equation
mathsolve exponential equationnumerical approximationexponential equation solutionnatural logarithm method
Solution:
The given equation to solve is:e^(4 - 7x) + 11 = 20First, isolate the exponential term by subtracting 11 from both sides:e^(4 - 7x) + 11 - 11 = 20 - 11e^(4 - 7x) = 9Now, to solve for x, apply the natural logarithm (ln) to both sides, because ln(e^y) = y:ln(e^(4 - 7x)) = ln(9)This simplifies to:4 - 7x = ln(9)Now, isolate x by subtracting 4 from both sides, and then divide by -7:4 - 7x - 4 = ln(9) - 4-7x = ln(9) - 4x = (ln(9) - 4) / (-7)Using a calculator to find the numerical approximation for ln(9):x ≈ (2.1972 - 4) / (-7)x ≈ (-1.8028) / (-7)x ≈ 0.25754Therefore, the solution to the equation is approximately x ≈ 0.25754.
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