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What is a log scale?

Highlighted from a real textbook passage. Explained by Clicked.

Used in a sentence

University Course Reader · STEM

Plotted on a log scale, the outbreak’s early weeks appear as a straight line rather than a flat one.

The reader highlighted one word in a textbook passage. Clicked broke down the concept “log scale” into plain English:

Explained in three depths

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Overview

A log scale is a chart axis where each step multiplies instead of adding. An ordinary axis climbs 100, 200, 300. A log axis climbs 10, 100, 1,000, usually multiplying by ten each time, and those marks sit the same distance apart. It exists for data where the smallest and largest numbers are wildly different, because an ordinary chart flattens everything small against the bottom.
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Overview

On a log scale, one step up means times ten, not plus ten. So 1, 10, 100 and 1,000 end up evenly spaced, which feels wrong until the day you need it. Plot the same figures the normal way and everything small gets pressed into the baseline where nobody can see it. The chart is not being difficult, it has simply run out of room. 😎

A quick take — often all you need.

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Detail

A company goes from 40 users to 400,000 over five years. Draw that normally and the first three years lie flat along the bottom. The axis has to reach 400,000, so 40 and 400 land almost on top of each other. Give every tenfold jump the same height and all five years become visible, because 40 to 400 now takes as much space as 40,000 to 400,000. Why not plot the real numbers? Because the real numbers hide what you usually want, which is how fast the figure is multiplying. Steady multiplying draws as a straight line here, and the steepness of that line is the rate. The trade-off is that height no longer tells you size at a glance, so the axis has to be read. Earthquakes, sound in decibels and pH are all measured this way.
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Detail

Your TikTok following goes 40, 400, 4,000, 40,000 over four months. Chart that the usual way and months one to three look like you did nothing at all. You did not do nothing. The chart is lying by omission. The axis has to stretch to 40,000, so everything smaller gets flattened. On a log scale each tenfold jump gets the same height, so all four months show up as the same size step, which is fair because each one was a tenfold jump. Why not use the real numbers? Because they bury the thing you actually care about, which is how fast it multiplies. One catch: a line that looks calm on here can still be describing something moving very quickly. Noise level in decibels runs on this too, as did every outbreak graph a few years back. 😎

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Analogy

Camera settings work like this. Each step of exposure lets in twice the light of the one before, so the settings run 1, 2, 4, 8, 16. Photographers call each of those one step, even though the amount of light keeps doubling. Nobody says a photo is 4,096 units bright. The useful question is how many doublings away it sits from where you started.
Deepest level reached.
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Analogy

Game levels pull this trick. Level 1 to 2 takes an afternoon, level 40 to 41 takes a week, yet the progress bar shows them as identical steps. That is deliberate, because nobody wants a bar where the first thirty levels are one pixel wide and the rest is empty space. The bar is measuring progress by each increase in difficulty, not by the hours it took to get there, which is the same idea behind a log scale. 😎
Deepest level reached.

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AI explanations may contain errors · Not professional advice

Formal definition — The same term, explained the usual way

A logarithmic scale represents values by their logarithm, so that equal distances along the axis correspond to equal ratios rather than equal differences. It is used where data span several orders of magnitude, and it renders exponential relationships as straight lines whose gradient is the growth rate, at the cost of visually compressing absolute differences at the upper end of the range.

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