Question - Solving Exponential Equation
Solution:
The equation provided in the image is:$$ e^{4x} - 7x + 11 = 20 $$To solve for $$ x $$, follow these steps:1. Isolate the exponential term by moving all other terms to the other side of the equation:$$ e^{4x} = 20 - 11 $$2. Simplify the right side:$$ e^{4x} = 9 $$3. Take the natural logarithm of both sides to remove the exponential:$$ \ln(e^{4x}) = \ln(9) $$4. Knowing that $$ \ln(e^y) = y $$, simplify the left side:$$ 4x = \ln(9) $$5. Finally, solve for $$ x $$ by dividing both sides by 4:$$ x = \frac{\ln(9)}{4} $$Therefore, the solution to the equation is:$$ x = \frac{\ln(9)}{4} $$
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