Evaluate natural log of 1/3

Problem

ln(1/3)

Solution

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

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

3. Substitute the values a=1 and b=3 into the rule.

4. Simplify the expression using the property that ln(1)=0

Final Answer

ln(1/3)=−ln(3)

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