Solve for x 3e^(-5x)=132

Problem

3*e(−5*x)=132

Solution

1. Isolate the exponential term by dividing both sides of the equation by 3

e(−5*x)=132/3

e(−5*x)=44

2. Apply the natural logarithm ln() to both sides to undo the exponential function.

ln(e(−5*x))=ln(44)

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

−5*x=ln(44)

4. Solve for x by dividing both sides by −5

x=ln(44)/(−5)

5. Rewrite the expression to place the negative sign in front of the fraction.

x=−ln(44)/5

Final Answer

x=−ln(44)/5

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