Question - Solving Exponential Equation for x
Solution:
The equation provided is:\[ e^{4 - 7x} + 11 = 20 \]To solve for $$ x $$, follow these steps:1. Subtract 11 from both sides of the equation:\[ e^{4 - 7x} = 9 \]2. Take the natural logarithm (ln) of both sides:\[ \ln(e^{4 - 7x}) = \ln(9) \]3. Because the natural logarithm and the exponential function are inverse operations, $$ \ln(e^{y}) = y $$. Hence:\[ 4 - 7x = \ln(9) \]4. To isolate $$ x $$, subtract 4 from both sides:\[ -7x = \ln(9) - 4 \]5. Finally, divide both sides by -7 to solve for $$ x $$:\[ x = \frac{\ln(9) - 4}{-7} \]So,\[ x = \frac{4 - \ln(9)}{7} \]Now you can use a calculator to find the approximate value of $$ x $$.
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