Question - Solving Exponential Equation for x
Solution:
The equation you provided is:e^(4 - 7x) + 11 = 20To solve for x, follow these steps:1. Isolate the exponential expression on one side of the equation:e^(4 - 7x) + 11 - 11 = 20 - 11e^(4 - 7x) = 92. Take the natural logarithm (ln) of both sides to eliminate the base e:ln(e^(4 - 7x)) = ln(9)Since ln(e^y) = y for any y, the left side simplifies to 4 - 7x. So we have:4 - 7x = ln(9)3. Solve for x:-7x = ln(9) - 4x = (ln(9) - 4) / (-7)x = (2.197224577 - 4) / (-7)4. Calculate the value of x. Please use a calculator to find the precise value:x ≈ (2.197224577 - 4) / (-7)x ≈ -1.802775423 / -7x ≈ 0.257539346So the solution to the equation is approximately x ≈ 0.257539346.
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