Nothing accelerated. The axis did.

The same growth, unequally drawn

Take an illustrative share at ₹50 that doubles once a year: ₹100, ₹200, ₹400, ₹800, ₹1,600. Every year is identical in the only measure an investor earns in — the rate.

In rupees the years are not identical at all. The first doubling adds ₹50. The last adds ₹800, sixteen times as much. A linear axis is ruled in rupees, so it hands out its height in the same proportion.

On an axis running to ₹1,600, the first year gets 3.1% of the height and the last gets 50%. Four fifths of the story is squeezed into the bottom sliver of the chart, and the reader concludes that something changed in the final year. Nothing did.

Straight means steady

This is the reading skill the axis buys you. On a logarithmic price axis, the slope of a line is the rate of return. A straight line means the rate held steady. A line bending upward means the rate itself increased. A line bending down means growth slowed, even while the price kept rising.

It also makes two periods comparable. Two stretches drawn at the same angle compounded at the same speed, whether the price was ₹60 or ₹6,000 at the time. On a linear axis that comparison is impossible by eye, because the later stretch is drawn with more ink for the same achievement.

The effect grows with the span. Over a month, the two axes draw nearly the same picture. Over a decade, a linear axis flattens everything except the most recent stretch into a line along the bottom.

How large this gets in a real index

India has a public example. The S&P BSE Sensex was set at a base value of 100 for the base year 1978-79, and it now trades in five figures — check the current level with the exchange rather than trusting a number in any article, including this one.

Put the whole history on a linear axis. The move from 100 to 200 — a doubling, and a year or more of Indian corporate history — occupies a fraction of one percent of the chart's height. It is thinner than the line drawn over it. Every crisis and recovery before the last stretch is compressed into the same invisible band.

The data is complete and correct. The axis is what hid it. This is why long-horizon charts in research notes are usually drawn logarithmically, and why a long linear chart tends to be a picture of the present pretending to be a picture of the past.

Where 'mandatory' ends

A logarithmic axis is required when the question is about rate over a long span. It is not a better axis in general, and there are questions it answers badly or cannot answer at all.

It cannot show zero or a negative number. The logarithm of zero is undefined, so anything that crosses zero — a profit-and-loss series, an indicator that oscillates around zero, a spread that can turn negative — must be drawn linearly.

It is the wrong axis for rupee amounts. If your question is how much money a ₹50,000 position gained, or how far apart two order prices sit, the linear axis answers directly and the logarithmic one makes you work.

Levels and lines do not transfer between the two. A straight trendline drawn on a logarithmic chart is a constant-rate line; drawn on the same data linearly it becomes a curve, and the reverse is also true. A trendline, channel or angle copied from one scale to the other is no longer the same line. Say which scale a drawn line was made on, or do not rely on it.

Both axes so far have been honest about the numbers printed beside them. The next distortion does not touch the axis at all — it changes the shape of the box the chart is drawn inside.