Expand the Logarithmic Expression natural log of (e^3)/5

Problem

ln((e3)/5)

Solution

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

ln((e3)/5)=ln(e3)−ln(5)

2. Apply the power rule for logarithms to the first term, which states that ln(ak)=k*ln(a)

ln(e3)−ln(5)=3*ln(e)−ln(5)

3. Simplify the expression using the property that the natural log of e is 1 so ln(e)=1

3*(1)−ln(5)=3−ln(5)

Final Answer

ln((e3)/5)=3−ln(5)

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