Logarithmic scales exist for data that runs from very small to very large values, such as 10 to 10 million.
On a normal axis, the largest values push everything else into a thin strip near 0.
A log axis gives each multiplication by 10 the same space, so small and large values both stay readable.
The axis is labelled with the original values, such as 10, 100 and 1,000, not with their logarithms.
Equal distances now mean equal ratios: going from 10 to 100 looks the same as going from 1,000 to 10,000.
A straight line on a log axis means growth by a constant percentage, such as 10% a month.
That makes log scales the standard way to compare growth rates of things of very different sizes.
2 lines with the same slope on a log axis are growing at the same percentage rate, whatever their sizes.
Base 10 is the usual choice for axes, though base 2 suits data that doubles.
Zero and negative values have no logarithm, so they cannot appear on a log axis at all.
Many readers misread log charts, seeing a flattening line as a fall, or a short gap as a small difference.
For a general audience, a log chart needs a clear label and often a note explaining what equal steps mean.
In practice, log scales suit incomes, populations, website traffic and anything that grows by percentages.
Histograms of skewed data often look far more even on a log scale, which also shows the tail clearly.
The usual mistake is using a log scale without saying so, which makes huge differences look modest.