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Logarithmic Scale
A log scale (short for logarithmic scale) is a way of displaying numerical data that uses the logarithm of values instead of the values themselves. This means:
- On a linear scale, equal distances represent equal increments (e.g., 1, 2, 3, 4...).
- On a log scale, equal distances represent multiplicative increments (e.g., 1, 10, 100, 1000... if using log base 10).
Why use a log scale?
- Handle wide ranges: Useful when data spans several orders of magnitude (e.g., 1 to 1,000,000).
- Reveal exponential trends: Exponential growth appears as a straight line on a log scale.
- Compress large values: Makes plots more readable when large values would otherwise dominate.
Example
| Value | Log10(Value) |
|---|---|
| 1 | 0 |
| 10 | 1 |
| 100 | 2 |
| 1000 | 3 |
A plot of these values on a log scale would space 1, 10, 100, and 1000 equally, even though their actual differences are large.