Solve for x 500e^(-x)=300

Problem

500*e(−x)=300

Solution

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

e(−x)=300/500

2. Simplify the fraction on the right side.

e(−x)=3/5

3. Apply the natural logarithm to both sides to eliminate the base e

ln(e(−x))=ln(3/5)

4. Use the property ln(eu)=u to simplify the left side.

−x=ln(3/5)

5. Solve for x by multiplying both sides by −1

x=−ln(3/5)

6. Apply the logarithm property −ln(a)=ln(a(−1)) to simplify the expression further.

x=ln(5/3)

Final Answer

x=ln(5/3)

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