Evaluate 2 natural log of e^5

Problem

2*ln(e5)

Solution

1. Identify the expression as a logarithmic term involving the natural logarithm ln(x) which has a base of e

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

2*ln(e5)=2⋅5*ln(e)

3. Simplify the product of the constants.

2⋅5*ln(e)=10*ln(e)

4. Evaluate the natural logarithm of e noting that ln(e)=1 because e1=e

10⋅1=10

Final Answer

2*ln(e5)=10

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