Evaluate natural log of 1/2

Problem

ln(1/2)

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=2 into the rule.

ln(1/2)=ln(1)−ln(2)

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

ln(1/2)=0−ln(2)

5. Simplify the resulting expression.

ln(1/2)=−ln(2)

Final Answer

ln(1/2)=−ln(2)

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