Trendline and channel construction on linear versus log scales

Scale belongs in the construction

A trendline is a constructed line through successive highs or lows used to mark a directional path that later price action can hold or break. A price channel is a second line translated from a trendline to bound the opposite side of a move. That corridor is testable only if the copied slope remains geometrically consistent.

Chart-scale analysis is the construction choice between linear and logarithmic price axes. It changes how equal point moves versus equal percentage moves appear, and how lines behave when they are shifted.

What linear and logarithmic axes do to distance

On a linear-scale price axis, equal point increments occupy equal vertical distance, so larger absolute ranges take more space even when the percentage change is unchanged. The vertical span from 50 to 100 is twice the span from 25 to 50, even though both moves are 100 percent changes. The same linear vertical distance can represent a 100 percent rise from 5 to 10 and a 5 percent rise from 100 to 105.

A semilogarithmic-scale chart pairs a linear time axis with a logarithmic price axis so that equal percentage changes occupy equal vertical distance. On a logarithmic price axis, the 100 percent rise from 25 to 50 occupies the same vertical distance as the 100 percent rise from 50 to 100. A 20 percent five-point rise from 25 to 30 occupies twice the vertical distance of a 10 percent five-point rise from 50 to 55.

When the two scales look alike

When a chart's overall price change stays modest, including ranges up to about 50 percent, the on-screen difference between linear and logarithmic price axes is often hard to see. Daily charts are commonly left on linear scaling when ranges stay limited, while weekly and monthly charts more often use logarithmic scaling because those horizons tend to cover larger percentage moves.

Fitting a line under a large advance

On a linearly scaled monthly chart of a large 1996 to 2000 advance, a straight linear trendline could not be fitted under the rise, while a logarithmic-trendline tracked that rise as support.

Placing the same monthly series on a logarithmic price axis lets a linear trendline sit under the 1996 to 2000 rise, and the logarithmic-trendline appears straight because the axis compensates its curve. A logarithmic-trendline is fitted so percentage distance, not raw point distance, stays comparable across a wide price range and remains consistent when the line is moved to form a channel.

Copying the slope into a channel

Shifting both lines upward to test a price channel keeps the logarithmic-trendline slope consistent at each height, whereas a linear trendline changes inclination as it enters a different price range.