A logarithmic scale is multiplicative instead of additive like a linear scale. Each unit you move multiplies or divides by a fixed amount instead of adding or subtracting. This makes it possible to see data that’s both really big and really small at the same time, and makes it easier to see structure in some kinds of plots. Click on the GIF to open the graph.

## Getting Started

To set either axis to a logarithmic scale, click on the wrench icon in the top left corner of the graph to open the graph settings menu or type CTRL + ALT + G. From there, open the ‘More Options’ section and change one or both axes from linear to logarithmic.

## Additional Information

When an axis is set to a logarithmic scale, you’ll notice some interesting patterns. First, you’ll find that cycles repeat every power of 10. So the lines between 1 and 10 are exactly the same distance as between 10 and 100, or 100 and 1000. Second, within those, lines get closer together as your numbers increase:

Since every line represents a common multiple instead of a common factor, the distance from 10 to 20 is the same as the distance from 20 to 40, or 40 to 80, or 1000 to 2000. You’ll notice that lines that are evenly spaced (10, 20, 30) on a linear plot are unevenly spaced on a logarithmic plot, getting narrower as you increase, until you reach 100, at which point it resets. You’ll also notice that the logarithmic values can get very small by zooming or panning, but they never reach 0 in the x- or the y-direction. Besides making it easier to display data that spans many orders of magnitude, logarithmic scales can also help to visualize the behavior of certain kinds of curves. Because there is a sense in which logarithms transform multiplication and division into addition and subtraction, logarithmic scales can plot multiplicative change in a way that appears linear. For example, exponential functions appear linear when the y-axis is logarithmic, and power functions appear linear when both axes are logarithmic. This might help you compare or reason about key features of different functions.

## Explore

Visualize relationships more easily with this graph that compares the diameter of each planet to its mass.

Open this graph and listen to the curve with audiotrace when both axes are set to a linear scale. Then change both axes to a logarithmic scale and listen to the curve with audiotrace again. (To use audiotrace, focus line 1 in the expression list, and type ALT + T and then type H to hear the graph).

## Learn More

- Log Mode
- Nonlinear Regression
- Unrepresentable Regression Parameters
- Tables
- Why am I seeing a negative R^2 value?

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