Evaluate natural log of 1/e

Problem

ln(1/e)

Solution

1. Rewrite the fraction using a negative exponent.

1/e=e(−1)

2. Substitute the exponential form back into the natural logarithm.

ln(e(−1))

3. Apply the logarithm power rule, which states ln(ab)=b*ln(a)

−1⋅ln(e)

4. Simplify using the property that the natural log of e is 1

−1⋅1=−1

Final Answer

ln(1/e)=−1

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