Graph natural log of (x)^3

Problem

ln(x3)

Solution

1. Apply the power rule for logarithms to simplify the expression.

ln(x3)=3*ln(x)

2. Identify the domain of the function. Since the argument of a natural logarithm must be positive, x3>0 implies x>0

D:(0,∞)

3. Determine the vertical asymptote by finding where the argument is zero.

x=0

4. Find the x-intercept by setting the function equal to zero.

3*ln(x)=0

ln(x)=0

x=e0=1

5. Analyze the behavior of the graph. Since the coefficient 3 is positive and the base e is greater than 1 the function is strictly increasing. Compared to the parent function ƒ(x)=ln(x) this graph is vertically stretched by a factor of 3

6. Plot key points to sketch the curve.

If *x=e,y=3*ln(e)=3

If *x=1/e,y=3*ln(e(−1))=−3

Final Answer

y=ln(x3)

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