Solve for x 14e^(3x+2)=560

Problem

14*e(3*x+2)=560

Solution

1. Isolate the exponential term by dividing both sides of the equation by 14

e(3*x+2)=560/14

e(3*x+2)=40

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

ln(e(3*x+2))=ln(40)

3*x+2=ln(40)

3. Isolate the term containing x by subtracting 2 from both sides.

3*x=ln(40)−2

4. Solve for x by dividing both sides by 3

x=(ln(40)−2)/3

Final Answer

x=(ln(40)−2)/3

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