Graph natural log of 7x

Problem

y=ln(7*x)

Solution

1. Identify the domain of the function. Since the argument of a natural logarithm must be positive, we set 7*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(7*x) gives e0=7*x which simplifies to 1 = 7x,o*r = \frac{1}{7}$.

4. Calculate additional points to determine the shape. For example, if x=1 y=ln(7)≈1.95 If x=e/7≈0.39 y=ln(e)=1

5. Sketch the curve starting from the vertical asymptote x=0 passing through (1/7,0) and increasing slowly as x increases.

Final Answer

y=ln(7*x)

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