When to Use a Log Scale (and When It Hides the Story)

The same revenue curve looks explosive on a linear axis and reassuringly steady on a log axis. Both charts show the same numbers; they answer different questions. The linear chart answers "how much bigger?" — the log chart answers "how much faster?" Most log-scale controversies are really question controversies: the chart is honest, the reader just brought a different question than the author answered.

What a Log Scale Actually Shows

On a log axis, equal distances are equal ratios: the gap from 10 to 100 looks the same as from 100 to 1,000. Consequences worth internalizing:

• Constant growth rates become straight lines. Revenue growing 10% monthly is a straight line on a log chart and an accelerating curve on a linear one. If the question is "is growth accelerating or slowing?", the log chart answers at a glance; the linear chart always looks like acceleration.
• Small values become visible. A series spanning 5 to 50,000 crushes everything under 1,000 into the linear axis. The log chart gives small and large regimes equal visual room.
• Absolute drama disappears. The jump from 40,000 to 50,000 — ten thousand real dollars — looks tiny next to the early jump from 40 to 50. If the decision depends on absolute amounts (cash, capacity, headcount), the log chart understates what matters.

Rules for Choosing Honestly

Use a log scale when the data spans multiple orders of magnitude and the interesting variation is proportional: growth rates, latency distributions, income data, network effects. Use a linear scale when the audience reasons in absolute units: budgets, headcounts, units shipped, anything where "how many more?" is the decision input. And when in doubt, show both — the linear chart for magnitude, the log chart for rate. Two small charts beat one ambiguous one.

Label aggressively. A log axis without a clear "log scale" annotation is a trap for casual readers, who will parse it as linear and conclude growth has stalled. Conversely, never log-scale a narrow range (say 80–120): with no orders of magnitude to tame, the log transform buys nothing and costs comprehension. The chart taxonomy rule applies doubly here: the axis is part of the chart's claim about what matters.

The Zero Problem

Log of zero is undefined, so log scales cannot show zeros — and datasets are full of them (days with no sales, users with no sessions). Common fixes, ranked by honesty: symlog or log1p transforms (plot log(1+x), linear near zero) when zeros are genuine data; annotated gaps when zeros mean "not measured"; and never silently dropping zero rows, which amputates the worst days from a performance chart. Whatever you choose, say so in a footnote — the transform is part of the methodology, like the missing-data decision it often accompanies.