Evaluate natural log of 3e^2

Problem

ln(3*e2)

Solution

1. Identify the expression as the natural logarithm of a product, which is written as ln(3*e2)

2. Apply the product rule for logarithms, which states that ln(a*b)=ln(a)+ln(b)

ln(3*e2)=ln(3)+ln(e2)

3. Apply the power rule for logarithms to the second term, which states that ln(xn)=n*ln(x)

ln(e2)=2*ln(e)

4. Simplify using the property that the natural logarithm of e is 1 so ln(e)=1

2*ln(e)=2*(1)=2

5. Combine the terms to reach the final simplified form.

ln(3)+2

Final Answer

ln(3*e2)=ln(3)+2

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