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Semi-log paper pairs a linear axis with a logarithmic one — the X-axis is evenly spaced like ordinary graph paper, while the Y-axis compresses each power-of-ten range (each "decade") into an equal band, with the lines inside each decade spaced according to log10. That makes it the right tool whenever a quantity grows or decays exponentially: population and bacterial growth curves, radioactive decay, compound interest, and frequency-response (Bode) plots all read as straight or smoothly curved lines on semi-log paper where they'd be unreadable curves on linear paper.
Set how many decades the Y-axis spans (2 to 5), and the X-axis spacing separately, in real millimeters. More decades let you plot a wider range of magnitudes on one page at the cost of less vertical resolution per decade; fewer decades give more detail within a narrower range. Choose US Letter or A4 and adjust line weight so the major decade lines stay visually distinct from the internal log-scale gridlines.
Plotting data where one quantity changes exponentially against a linear one — growth and decay curves, frequency response plots, and any data spanning multiple orders of magnitude on one axis.
Match it to the range of your data: if your Y-values span from 1 to 1,000, that's 3 decades. Add an extra decade of headroom if you're not sure your data will stay within range.
Semi-log has one linear axis and one logarithmic axis; log-log has both axes on a logarithmic scale. Use log-log when both variables span multiple orders of magnitude — for example, power-law relationships.
The Y-axis (vertical) is logarithmic; the X-axis (horizontal) is linear, matching the conventional layout used in most textbooks and lab manuals.