Question - Solving Exponential Equation
Solution:
This is an exponential equation. Let's solve it step by step:The equation is `e^(4-7x) + 11 = 20`.First, subtract 11 from both sides to isolate the exponential term:`e^(4-7x) = 9`.Next, we'll take the natural logarithm (ln) of both sides to get rid of the exponential expression and solve for x:`ln(e^(4-7x)) = ln(9)`.Using the property of logarithms:`4 - 7x = ln(9)`.Now, we just need to solve for x:`-7x = ln(9) - 4`.Divide both sides by -7 to solve for x:`x = (ln(9) - 4) / -7`.This gives you the value of x in terms of the natural logarithm of 9. Use a calculator to find a numerical value if required.
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