Log axes
Pick a data set, then press the two buttons to switch each axis between an ordinary (linear) scale and a log scale. Your job is to find the pair of axes that makes the points fall on a straight line. When they do, a line is fitted and its slope is explained. Before you press anything, guess: which axes will straighten this one?
What's going on
On a log axis, equal steps mean equal multiples: 1, 10, 100, 1000 are evenly spaced. Plotting on a log axis is the same as plotting the logarithm of the number.
Log on y only. If y = A × gˣ (multiply by g at every step), then log y = log A + x log g. That is a straight line in x, with slope log g. So exponential growth is straight on a log y-axis, and the slope gives the growth factor: g = 10 to the power of the slope.
Log on both. If y = A × xᵖ (a power law), then log y = log A + p log x. That is a straight line in log x, and the slope is the power p itself.
Neither. If the points are already straight on ordinary axes, the rule is y = mx + c and nothing needs a logarithm.
The number r² measures how close the points are to a line: 1 means exactly on it. Here the line is drawn once r² reaches 0.99. A warning: over a short range almost any curve looks straight, so data that covers many multiples is what makes a log plot convincing.
Sheets: Straight lines hiding in curved data, Fifty years of doubling and The few that are huge.