Simplify/Condense natural log of 6/(e^2)

Problem

ln(6/(e2))

Solution

1. Identify the logarithmic property for quotients, which states that ln(a/b)=ln(a)−ln(b)

2. Apply the property to the expression by splitting the natural log of the fraction into the difference of two natural logs.

ln(6/(e2))=ln(6)−ln(e2)

3. Simplify the second term using the inverse property of logarithms, ln(ex)=x

ln(e2)=2

4. Combine the results to reach the final condensed form.

ln(6)−2

Final Answer

ln(6/(e2))=ln(6)−2

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