Simplify/Condense natural log of 5e^3

Problem

ln(5*e3)

Solution

1. Identify the property of logarithms for products, which states that the logarithm of a product is the sum of the logarithms: ln(a*b)=ln(a)+ln(b)

2. Apply the product rule to the expression by splitting the natural log of 5 and e3

ln(5*e3)=ln(5)+ln(e3)

3. Apply the power rule for logarithms, which states ln(xn)=n*ln(x) to the second term.

ln(5)+ln(e3)=ln(5)+3*ln(e)

4. Simplify the expression using the fact that the natural log of e is 1

ln(5)+3*(1)=ln(5)+3

Final Answer

ln(5*e3)=ln(5)+3

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