Simplify/Condense natural log of 3- natural log of 1

Problem

ln(3)−ln(1)

Solution

1. Identify the logarithmic property for subtraction, which states that the difference of two logarithms with the same base is the logarithm of the quotient of their arguments.

ln(a)−ln(b)=ln(a/b)

2. Apply the formula to the given expression by substituting a=3 and b=1

ln(3)−ln(1)=ln(3/1)

3. Simplify the fraction inside the natural logarithm.

3/1=3

4. Evaluate the specific term ln(1) noting that the natural log of 1 is always 0

ln(1)=0

5. Subtract the values to find the final condensed form.

ln(3)−0=ln(3)

Final Answer

ln(3)−ln(1)=ln(3)

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