LOG10 reports how many powers of 10 make a positive number. For example, 1000 equals 10 cubed, so LOG10(1000) equals 3. For an explicitly chosen alternative base, use LOG instead.

Official Apple syntax: LOG10(pos-num). This guide uses the Apple Functions Help 15.4 entry, inspected on 2026-10-11. The documentation version identifies this help edition; it does not prove which Apple Numbers release first supported the function. The examples are mathematically expected results, not recorded runs from the Numbers application.

An analyst wants to express ratios on an orders-of-magnitude scale. Powers of 10 make the behavior especially easy to verify. If your goal is to compare values in a large table, first check the data type and the mathematical transformation you need. Logarithms change scale and do not simply reformat numbers; the exponential function reverses the natural-log transformation for valid inputs.

=LOG10(pos-num)

The sole input must be strictly greater than zero. LOG10 cannot return a real-number logarithm for zero or a negative input. Apple documents LOG as the alternative when another base is required. Apple’s official page defines these limits and any defaults: function reference. For input types and cross-table references, consult Apple’s value-type reference.

Decimal separators and locales: Apple’s English examples separate arguments with commas and use a decimal point in numbers. Apple says to use semicolons between arguments if your system uses a decimal comma. For example, a decimal-comma locale may enter 0,5 as a numeric input where the English examples use 0.5. This function has only one argument, so no argument separator is used in the basic formula. Nested two-argument functions may require semicolons when the decimal separator is a comma. Use the formula editor to insert references. See Apple’s official functions overview.

1. Open a new Numbers document and make one table called Logarithm Lab. Mark row 1 as a header.
2. Put Input in B1; put Result in C1. Copy the numbers shown below into B2:B7 as actual numbers, not text.
3. Enter the formula in C2, then fill down through C7; the B-row reference changes automatically as you fill. Format the result cells to show six decimal places for comparison.
4. Compare the results to the independent expectations. Small final-digit differences are possible when software uses floating-point arithmetic; integer-looking results below are mathematical exact values for the chosen inputs, not native Numbers screenshots.

These displayed values were calculated independently using Python’s math functions, then rounded to six decimal places for display. Do not interpret them as six-decimal internal precision in Numbers. Values may display differently under General, Scientific, or region-specific number formats.

If your result is in another table: selecting the input cell while editing the formula lets Numbers insert a qualified reference, such as Logarithm Lab::B2; do not assume unqualified B2 refers to the intended table in a multi-table document. See Apple’s reference-value examples. Relative references normally adjust when filled; confirm formula references after moving or copying cells.

Compare orders of magnitude

If B12 = 100 and C12 = 100000, =LOG10(C12/B12) returns 3. That says the latter is 10 cubed, or 1000 times, as large.

Power-ratio decibels (defined convention)

A power ratio uses =10*LOG10(C13/B13) for two positive power values. If B13 = 10 and C13 = 100, the result is 10 dB. This is the standard definition for a power ratio, not a rule for all physical quantities (amplitudes use a different multiplier).

Equivalent built-in calculation

=LOG(100,10) and =LOG10(100) each give 2. The functions are not separate mathematical bases: LOG10 is the specialized base-10 case of LOG.

• Need a base other than 10: LOG10 does not accept a second argument. Use =LOG(B2,2) for base 2.
• Ratio smaller than 1 looks negative: A positive value below 1 correctly has a negative base-10 logarithm.
• Zero or negative inputs: These are outside Apple’s documented domain; inspect the inputs before calculating.
• Unexpected error from imported values: confirm the inputs are numeric and satisfy the documented domain. A string that looks like "100" is not the same as a confirmed numeric value. Apple distinguishes number values from string values in its value-type glossary.
• A formula gives a surprising output after copying: inspect its relative cell addresses and table qualification. When the formula refers to another table, Numbers uses :: separators, as described in Apple’s documentation.
• Displayed digits differ slightly from the expected table: the six-decimal columns are rounded for readability. Apple’s functions may compute using floating-point arithmetic, and even mathematical inverses can disagree in their low-order digits.
• Formula rejected in a non-English locale: verify the region’s decimal symbol and argument separator. Use Numbers’ formula editor rather than assuming pasted Excel or English syntax is universally accepted.
• Extreme inputs or app-specific errors: this guide does not assert a particular error-code spelling, overflow threshold, coercion policy or first-supported release because no native Numbers installation was available for testing.

Excel also documents LOG10(number) as the base-10 logarithm of a positive real number. Apple and Excel have the same core mathematics for the ordinary numeric examples; imported types, numeric precision and app-specific error displays were not tested. Microsoft documents the Excel counterpart in its official LOG10 reference, checked 2026-10-11. This confirms the ordinary mathematical operation, not identical handling of every empty cell, invalid string, floating-point boundary or user locale.

This batch has not executed the formulas in Google Sheets or verified Sheets-specific coercion, error strings, or platform/version behavior. Before copying a large production workbook, test representative values in the destination app and verify the imported cell types; similarly named formulas are not a guarantee of full parity.

• EXP

• Apple Numbers — function documentation
• Apple’s value-type reference
• Apple’s official functions overview
• EXP
• LN
• LOG

Verification status: Official documentation checked; example outcomes were independently reasoned or arithmetically checked where applicable. Not executed in Apple Numbers.

• No genuine Apple Numbers screenshots are included; this guide does not use mock application images.