Expand the Logarithmic Expression natural log of 1/2

Problem

ln(1/2)

Solution

1. Identify the logarithmic property for quotients, which states that the logarithm of a division is the difference of the logarithms.

ln(a/b)=ln(a)−ln(b)

2. Apply the formula to the given expression by setting a=1 and b=2

ln(1/2)=ln(1)−ln(2)

3. Simplify the expression by evaluating the natural log of 1, which is 0.

ln(1)=0

4. Substitute the value back into the expression to find the final expanded form.

0−ln(2)=−ln(2)

Final Answer

ln(1/2)=−ln(2)

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