Read logarithmic plots in Book Isle: interpret equal distances as ratios, not differences

A logarithmic plot can place positive values spanning a wide range on one graph, but equal distances no longer represent equal numerical differences. Locate a figure in Book Isle, record its axis names, ticks and caption, then check an invented example using 1, 10 and 100. The app need not recognise the chart or change its axes; calculations belong in your own record. Explain how this figure encodes numbers rather than judging research conclusions from a straight line, steep slope or compressed appearance alone.

Keep the complete figure context and source

Choose a legitimately available book with clear axes and caption. Record title, edition, chapter, figure number and a distinctive nearby phrase, bookmarking around the figure for return. For fixed PDF, retain printed page number and file-page index; for reflowable books, add a chapter anchor. Inspect the whole figure, including legend, external multipliers and footnotes, before magnifying its most striking curve. If ticks are unreadable, mark insufficient information and check the original file or a clearer legitimate copy instead of guessing from line positions. Search may not index image text, so missing search results do not mean ticks are absent; follow a figure-number reference from the prose.

Identify each axis scale separately

Record each axis’s name, unit, range and tick style separately rather than assuming both are logarithmic because one is. In the invented example, time 0, 1, 2 lies on a linear horizontal axis; positive quantities 1, 10, 100 lie on a base-10 logarithmic vertical axis. This is a semilog plot, not a log-log plot. Horizontal 0 is valid here because that axis is not logarithmic. If the base is unknown, check the caption or methods instead of guessing base 10 from uneven ticks. Broken axes, categorical axes and special transformations can also change spacing, so identify what the author actually states.

Compare ratios and differences for equal intervals

On paper or in your notes, draw three equally spaced horizontal marks labelled 1, 10 and 100. Adjacent ratios are both 10: 10/1=10 and 100/10=10. Their differences are 9 and 90, not equal. Read labels before calculating; equal spacing does not mean adding 10 each time. Compare with a linear axis containing the same values, where the second gap is much larger than the first. Change only the encoding, not the values. No drawing inside Book Isle is required; a written relation suffices. Retain original units: a ratio is dimensionless, while a difference retains the original unit. Do not merge them into one field.

Interpret midpoints multiplicatively

On a base-10 logarithmic axis, the spatial midpoint between 1 and 10 represents approximately 3.162, not the arithmetic mean 5.5: its square is about 10, giving approximately equal ratios on either side. Verify with your own calculator; the app need not calculate logarithms. Minor ticks at 2, 3, 4 and so on are not equally spaced as on a linear axis, so do not divide the visible interval into nine equal parts. For an unclear point, retain an approximation sign and reading range instead of reporting three-decimal precision from screen inspection. State the reading method before the estimate. This distinguishes coordinate encoding without proving a pattern in the underlying data.

Separate raw values from transformed numbers

If the vertical labels show original quantities 1, 10 and 100, record those quantities. If the author instead plots log10(y) with labels 0, 1, 2, mark them as transformed numbers and list the corresponding raw values separately. Do not interpret 0 as a raw quantity of zero: log10(1)=0. Check the base and variable units in the methods where necessary instead of assigning original units to transformed numbers arbitrarily. The two presentations may convey related information but require different axis names and reading statements. If copied image text loses superscripts or subscripts, verify the source. In particular, do not mistake a power of 10 for an ordinary two-digit number and then continue calculating.

Keep zero and negative values off an ordinary log axis

The ordinary logarithmic vertical axis in this exercise accepts positive values only; zero and negatives cannot be placed directly on it. If a figure appears to include a zero point, negative ticks or an accompanying table beginning at zero, check for another linear axis, a special symmetric transformation, shifted data or plotting of only a subset. Do not invent the author’s treatment or silently replace 0 with a tiny positive value to make plotting possible. Retain separate meanings for missing, below detection limit and true zero. This restriction concerns the log axis, not the example’s linear time axis beginning at 0. If the explanation remains unclear, retain the question and suspend numerical conclusions for that part.

Do not infer a research conclusion from straightness alone

The invented points at times 0, 1 and 2 with values 1, 10 and 100 can form a straight line on a semilog plot. We can state that successive values are ten times their predecessors, not infer perpetual real-world growth, causation or the next point from three invented values. For a published plot, recheck sample range, uncertainty, fitting description and caption qualifications. Before comparing apparent steepness across two figures, confirm matching ranges, aspect ratios and encodings; visual slopes cannot otherwise directly indicate numerical rates. Save the plotted observation separately from the author’s interpretation, preserving words such as may and only within this range rather than treating the compressed shape as all the evidence.

Finish with a verbal and exported-record check

Leave the figure and use the reading card alone to name the logarithmic axis and its base, then state both the increases and multiplication factors from 1 to 10 and from 10 to 100. Return to verify. If you describe equal additive increments, redo the ratio and difference fields. Save location, axis explanation, raw readings, estimate ranges and unresolved questions. Reopen an exported note copy to check decimal points, minus signs and power notation. A later log-log figure requires rechecking both axes rather than copying this example’s linear-time explanation. Completion means someone can return to the same figure and verify your reading, not that you endorse every conclusion in the book or paper.

Related tutorials and sources

Book Isle figure references: connect numbers, pages and reading notes; Follow worked examples in Book Isle: track symbols, units and substitutions.

Sources checked on 5 November 2026: the official Book Isle App Store listing and Apple Lookup show version 1.1.3, requiring iOS / iPadOS 15.6 or later. This workflow uses local reading, search, bookmarks and notes for manual checking. Readers record the samples and conclusions; automatic problem solving, experiment analysis or chart recognition is not assumed. Confirm available controls against the installed version and file type. The exercise does not claim step-by-step device testing in this batch.

Method reference: NIST WTT plot-axis documentation distinguishes linear, inverse and base-10 logarithmic coordinates. Only its coordinate concepts are used here; all values and reading-card steps are original. Its legacy software menus are not Book Isle controls.