Solve for x 2000=500e^(4x)

Problem

2000=500*e(4*x)

Solution

1. Isolate the exponential term by dividing both sides of the equation by 500

4=e(4*x)

2. Apply the natural logarithm ln() to both sides to eliminate the base e

ln(4)=ln(e(4*x))

3. Simplify the right side using the property ln(eu)=u

ln(4)=4*x

4. Solve for x by dividing both sides by 4

x=ln(4)/4

5. Simplify the expression further if desired by rewriting 4 as 2 and using the power rule for logarithms.

x=ln(2)/4

x=(2*ln(2))/4

x=ln(2)/2

Final Answer

x=ln(4)/4

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