Evaluate e^(7 natural log of x)

Problem

e(7*ln(x))

Solution

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

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

eln(x7)

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

4. Simplify the expression using the identity eln(u)=u

x7

Final Answer

e(7*ln(x))=x7

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