Solve for x 2e^(3x)=1

Problem

2*e^(3*x)=1

Solution

1. Isolate the exponential term by dividing both sides of the equation by 2

e^(3*x)=1/2

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

ln(e^(3*x))=ln(1/2)

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

3*x=ln(1/2)

4. Solve for x by dividing both sides by 3

x=ln(1/2)/3

5. Rewrite the expression using the logarithm quotient rule ln(1/a)=−ln(a)

x=−ln(2)/3

Final Answer

x=−ln(2)/3

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