Evaluate the Limit

Problem

(lim_x→e)(ln(x3))

Solution

1. Identify the limit expression and the value that x is approaching, which is e

2. Apply the power rule for logarithms to simplify the expression by moving the exponent 3 in front of the natural log.

(lim_x→e)(3)*ln(x)

3. Substitute the value x=e into the expression, since the natural log function is continuous at x=e

3*ln(e)

4. Evaluate the natural log of e knowing that ln(e)=1

3*(1)

5. Simplify the final result.

3

Final Answer

(lim_x→e)(ln(x3))=3

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