Graph natural log of 5x

Problem

y=ln(5*x)

Solution

1. Identify the domain of the function. Since the argument of a natural logarithm must be positive, we set 5*x>0 which means x>0

2. Determine the vertical asymptote by finding where the argument equals zero. As x approaches 0 from the right, y approaches −∞ so the vertical asymptote is x=0

3. Find the x-intercept by setting y=0 Solving 0=ln(5*x) gives e0=5*x which simplifies to 1 = 5x,s(o) = \frac{1}{5}o*r.2$.

4. Calculate additional points to determine the shape. For x=1 y=ln(5)≈1.61 For x=e/5≈0.54 y=ln(e)=1

5. Sketch the curve starting near the vertical asymptote x=0 passing through (0.2,0) and (1,1.61) and continuing to increase slowly as x increases.

Final Answer

y=ln(5*x)

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