Graph natural log of 8x

Problem

y=ln(8*x)

Solution

1. Identify the domain of the function. Since the argument of a natural logarithm must be positive, we set 8*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(8*x) gives e0=8*x which simplifies to 1 = 8x,o*r = \frac{1}{8}$.

4. Calculate additional points to determine the shape. For example, if x=e/8 then y=ln(e)=1 If x=1 then y=ln(8)≈2.08

5. Sketch the curve starting near the vertical asymptote x=0 passing through (1/8,0) and increasing slowly as x increases.

Final Answer

y=ln(8*x)

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