Free printable resources · Original practice
Keep one axis linear and make the other logarithmic. Compare exact growth and decay data, with the logarithmic axis clearly labeled.
Keep one axis linear and make the other logarithmic. Compare exact growth and decay data, with the logarithmic axis clearly labeled.
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Original blank grid. Letter or A4. Free PDF and SVG.
Original blank grid. Letter or A4. Free PDF and SVG.
The complete collection
Use the student pack first, then compare the reference or answer. Packs are PDFs; individual sheets below also include editable SVG files. The paper choice applies to every download.
Original task with a separate reference answer. Letter or A4.
Original task with a separate reference answer. Letter or A4.
| Task | Given pairs (x,y) | Worked result |
|---|---|---|
| SL01 | (0,1); (1,2); (2,4); (3,8); (4,16) | Multiplier 2. y=2^x. y(5)=32. log10(y) slope = log10(2). |
| SL02 | (0,100); (1,50); (2,25); (3,12.5); (4,6.25) | Multiplier 0.5. y=100*(1/2)^x. y(5)=3.125. log10(y) slope = -log10(2). |
SL01 uses y = 2ˣ, so log10(y) = x log10(2). At x = 0, y = 1; the point is allowed because x is on a linear axis. Four steps give 16 and the next step gives 32. SL02 uses y = 100(1/2)ˣ, so log10(y) = 2 − x log10(2). Its next value after 6.25 is 3.125.
| Layout | Horizontal range | Vertical range | A straight line means |
|---|---|---|---|
| Main log-y | x = 0–10, linear | y = 1–100, log10 | log10(y) is linear in x |
| Optional log-x | x = 1–100, log10 | y = 0–10, linear | y is linear in log10(x) |
The optional transposed blank is a separate coordinate layout, not a relabeling of the same data. Keep the names and numerical ranges of both axes with the chart. A logarithmic input must be positive; values such as 0.5 are valid mathematically but outside these particular 1–100 log ranges.
Begin by choosing the appropriate PDF or SVG file based on your data structure. The main blank features a linear x-axis ranging from zero to ten and a logarithmic y-axis spanning one to one hundred. This orientation suits exponential growth or decay where the independent variable is linear. If your data requires a logarithmic x-axis from one to one hundred and a linear y-axis from zero to ten, select the optional transposed blank instead. Ensure you download the Letter or A4 size that matches your printer settings. This initial selection prevents axis mismatch errors during plotting.
When plotting data, remember that zero is permitted on the linear axes but strictly excluded from the logarithmic axes. For the main blank, plot y-values between one and one hundred. Values below one are valid logarithmic inputs but fall outside the supplied range, so choose a chart with another labeled range; do not alter a value to make it fit. Use the provided worksheets SL01 and SL02 for practice. SL01 plots y equals two to the power of x, while SL02 plots y equals one hundred times one-half to the power of x. Mark each coordinate precisely to visualize the linear relationship on the log scale.
The supplied points come from exact exponential equations. On the main orientation, log10(y) is linear in x: SL01 has slope log10(2), about 0.30103, and SL02 has the opposite slope. For SL01, every increase of one in x doubles y; for SL02 it halves y. The next values are 32 and 3.125 respectively. A straight-looking plot of real observations alone does not establish an exact exponential law. Also read the axis orientation: on the transposed blank, a straight line instead expresses a linear relationship between y and log10(x).
| Watch for | Check instead |
|---|---|
| Plotting zero on the logarithmic axis | Zero is allowed only on the linear axes. The logarithmic axes range from one to one hundred, so ensure all y-values in the main blank are positive and within this range. |
| Using the main blank for logarithmic x-data | The main blank has a linear x-axis. If your independent variable requires a logarithmic scale from one to one hundred, switch to the optional transposed blank where x is log10 and y is linear. |
| Interpreting a straight line as a power relation | On the main blank, x is linear and y is logarithmic, so these exact exponential examples form straight lines. On the transposed blank, y is linear in log10(x). A power relationship is linear in log-log coordinates. Read both axis labels first. |
Choose the file matching the paper in your printer. Print the PDF at Actual size / 100%, turning off Fit, Shrink and browser headers. An SVG editor or browser can change its scale even though the file uses millimeter dimensions. Use the supplied calibration bars where present when a task depends on physical size; a screen preview alone does not establish printed size.
The packs contain the same individual pages in collection order. They are a convenient download, not extra different exercises. On coordinate plots, uniform scaling preserves the numerical positions relative to the axes. On image-copy tasks, keep the specified proportions and any stated source-to-target enlargement. Color is optional: labels, line positions and relative lightness also explain the references.
Positive sub-one values are valid logarithmic inputs mathematically, but they fall outside the supplied one to one hundred range on the main blank. You would need to adjust the scale or use a different template.
No. The data in worksheets SL01 and SL02 are synthetic and exact. They are designed to demonstrate exponential growth and decay patterns without claiming any real-world experimental trends or physical measurements.
The resource is available in both PDF and SVG formats. You can choose between Letter and A4 paper sizes to match your printer settings. No physical printer checks have been performed, so verify your output locally.
Yes. Every linked worksheet, PDF, SVG and answer is free without signup. Original Zumola resources use CC BY 4.0: credit Zumola, link the license and indicate changes. Analytics consent is not required to download or use them.
A semi-log sheet is only useful if the reader knows which axis is logarithmic. Write the axis name and the scale type at the end of each axis before placing the first point. On a logarithmic y-axis, mark the decade boundaries (1, 10, 100, and so on) and note that the spacing between 1 and 2 is wider than between 8 and 9. On the linear x-axis, mark equal intervals and state the unit.
A second check is the direction of growth. On a logarithmic axis, equal vertical distances represent equal multiplicative factors, not equal additions. If your data doubles, the vertical gap stays the same wherever you start. Confirm this by measuring two gaps that should match before you trust the rest of the plot.
Suppose a culture count is recorded at four times: at 0 hours the count is 5, at 1 hour it is 10, at 2 hours it is 20, and at 3 hours it is 40. The x-axis is linear in hours, so the points sit at equal horizontal spacing. The y-axis is logarithmic, so each doubling produces the same vertical gap.
To place 5 on a logarithmic axis between 1 and 10, use the logarithm rather than the arithmetic midpoint. Since log(5) is about 0.699 and log(10) is 1, the point for 5 sits above the halfway height of that decade. The values 10, 20, and 40 each move up by one equal doubling step. If your plotted gaps are unequal, the axis is probably linear by mistake or the labels are misread.
After plotting, run three quick checks. First, confirm no plotted value is zero or negative on the logarithmic axis, since those cannot be placed. Second, confirm the vertical gaps for equal multiplicative changes match. Third, confirm the axis labels state the scale type, not just the unit.
If the points form a straight line on a semi-log plot, the underlying relationship is exponential. If they curve, the relationship is not exponential, and you should not force a straight line through them. Record what you see rather than what you expect.
Plot the pairs (0, 5), (1, 10), (2, 20), (3, 40) on a semi-log sheet with a linear x-axis in hours and a logarithmic y-axis.
The x-axis is linear, so the points sit at equal horizontal spacing. The y-axis is logarithmic, so each doubling from 5 to 10, 10 to 20, and 20 to 40 produces the same vertical gap. Place 5 between 1 and 10 using logarithmic spacing: log(5) is about 0.699, above the arithmetic midpoint. The four points should form a straight line if the relationship is exponential.
No. A logarithmic axis cannot represent zero or negative values. Remove or transform such values before plotting.
Read the axis label. The logarithmic axis should state the scale type and show decade boundaries with unequal spacing between numbers.
A straight line indicates an exponential relationship between the variables, provided the axes are correctly labeled and scaled.
