Evaluate e^(2 natural log of x)

Problem

e(2*ln(x))

Solution

1. Identify the expression as a base e raised to a power involving a natural logarithm.

2. Apply the power rule of logarithms, which states a*ln(b)=ln(ba) to the exponent.

e(2*ln(x))=eln(x2)

3. Simplify using the inverse property of logarithms and exponents, where eln(u)=u

eln(x2)=x2

Final Answer

e(2*ln(x))=x2

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