Evaluate e^(7 natural log of x)

Problem

e^(7*ln(x))

Solution

1. Identify the logarithmic property a*ln(b)=ln(b^a) to rewrite the exponent.

2. Apply the property to the expression 7*ln(x) to move the coefficient into the exponent of the argument.

e^ln(x^7)

3. Recognize that the exponential function e^u and the natural logarithm ln(u) are inverse functions.

4. Simplify the expression using the identity e^ln(u)=u

x^7

Final Answer

e^(7*ln(x))=x^7

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