Solve for x e^(3x)=25

Problem

e(3*x)=25

Solution

1. Apply the natural logarithm to both sides of the equation to isolate the exponent.

ln(e(3*x))=ln(25)

2. Simplify the left side using the inverse property of logarithms, ln(eu)=u

3*x=ln(25)

3. Isolate x by dividing both sides of the equation by 3

x=ln(25)/3

4. Rewrite the expression using logarithm power rules, noting that 25=5 so ln(25)=2*ln(5)

x=(2*ln(5))/3

Final Answer

x=ln(25)/3

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