Graph a Logarithmic Function
The graph of y = log_b(x) crosses the x-axis at (1, 0), rises slowly to the right, and has a vertical asymptote at x = 0, because logarithms are only defined for x > 0.
At a glance
| What it is | Graph y = ln(x) and y = log(x) online. See the x-intercept (1, 0), the vertical asymptote x = 0 and the domain x > 0. Free graphing calculator. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| x-intercept | (1, 0) for every base |
|---|---|
| Vertical asymptote | x = 0 |
| Domain / range | x > 0 / all real numbers |
| Key points | ln: (1, 0) and (e, 1); log₁₀: (1, 0) and (10, 1) |
| Inverse of | The exponential y = bˣ |
What is the difference between ln and log?
ln(x) is the natural logarithm, base e ≈ 2.718. log(x) usually means base 10. Any base can be written with either: log_b(x) = ln(x) ÷ ln(b).
How to use it in Plotline
- The graph of y = ln(x) and y = log(x) is already loaded above. Edit the equation in the list to change it.
- Drag the graph to move around, scroll or pinch to zoom, and tap the crosshair to reset the view.
- Hover over or tap the curve to read the coordinates of any point.
- Press Enter to add another equation and compare graphs in different colors.
Frequently asked questions
Why is log(0) undefined?
No power of a positive base equals 0, so log(0) has no value. The graph approaches the asymptote x = 0 but never reaches it.
Is it free?
Yes. The graphing calculator is free with no account and no sign-up: plot as many equations as you like, use sliders, save graphs in your browser and share them by link. It installs as an app and keeps working offline.
Learn more
Related
- Exponential function – Graph exponential functions like y = 2ˣ and y = eˣ online.
- Square root function – Graph y = √x online and learn its domain, range and key points (0,0), (1,1), (4,2), (9,3).
- Log calculator – Free log calculator: find log base 10, natural log ln, log base 2 or any base.
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