Expand the Logarithmic Expression natural log of 1/e

Problem

ln(1/e)

Solution

1. Identify the expression as a natural logarithm of a quotient.

2. Apply the quotient rule for logarithms, which states ln(a/b)=ln(a)−ln(b)

ln(1/e)=ln(1)−ln(e)

3. Evaluate the natural logarithm of 1, knowing that ln(1)=0

ln(1/e)=0−ln(e)

4. Evaluate the natural logarithm of e knowing that ln(e)=1

ln(1/e)=0−1

5. Simplify the resulting arithmetic.

ln(1/e)=−1

Final Answer

ln(1/e)=−1

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