Simplify/Condense e^(3 natural log of x)

Problem

e^(3*ln(x))

Solution

1. Apply the power property of logarithms to the exponent, which states that a*ln(b)=ln(b^a)

ln(x^3)

2. Identify the inverse relationship between the natural exponential function e^x and the natural logarithmic function ln(x)

e^ln(u)=u

3. Simplify the expression by applying this inverse property to the term e^ln(x^3)

x^3

Final Answer

e^(3*ln(x))=x^3

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