Expand the Logarithmic Expression natural log of ex^3

Problem

ln(e*x3)

Solution

1. Identify the expression as a natural logarithm of a product of two terms, e and x3

2. Apply the product rule for logarithms, which states ln(a*b)=ln(a)+ln(b)

ln(e*x3)=ln(e)+ln(x3)

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

ln(e)+ln(x3)=ln(e)+3*ln(x)

4. Simplify the first term using the property that the natural log of e is 1

ln(e)+3*ln(x)=1+3*ln(x)

Final Answer

ln(e*x3)=1+3*ln(x)

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