Straightener

Each preset (Exponential, Power or Linear) has six points. Each point on the standard plot has an image on the semi-log plot $(x, \ln(y))$ and on the log-log plot $(\ln(x), \ln(y))$, and the images move with it. The point is connected to both images by leaders, thin lines drawn across the plots.

Each plot has a reference line through the first and last points. The vertical gap from every other point to the line is marked by a thin segment.

The log rule for each plot is listed in the panel:

$$\ln(Ce^{kx}) = \ln(C) + kx \qquad \ln(Cx^{k}) = \ln(C) + k\ln(x)$$

Both rules hold only for $C > 0$, and the log-log rule holds only for $x > 0$ as well. From the reference line’s slope $m$ and intercept $b$, $k = m$ and $C = e^{b}$, both worked out under Show numbers. Horizontal shift takes the smallest input as $h$, which puts the semi-log work in the horizontal-shift form $y = Ce^{k(x-h)}$. Then $b = \ln(y_{\text{first}})$ and $C = y_{\text{first}}$.

Points cannot be dragged to $x = 0$ or $y = 0$, because $\ln$ is defined only for positive numbers. Values can also be typed in the table.

Under More is a table of verdicts by plot type, and, with Show numbers on, the worked $m$ and $b$ of the standard plot’s reference line.

Keys: click the standard plot, then press 1 to 6 to pick a point. Press an arrow key to move it as far as one press of a minus or plus button. Hold Shift with an arrow key to move it five times as far. Press Esc to let go.