LN in Apple Numbers: Natural Logarithms and Growth Rates

LN finds the natural logarithm of a positive number: the exponent needed to raise e to that value. It is the inverse of EXP for positive inputs, but can introduce floating-point differences.

Official Apple syntax: LN(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.

A reporting analyst compares growth ratios. A natural-log transform gives a symmetric mathematical scale: increases above 1 have positive logs; ratios below 1 have negative logs. 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.

=LN(pos-num)

The input must be strictly positive according to Apple. Zero and negative real inputs are outside the documented domain; do not expect a numeric real-log result. 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.

Continuous rate from two values

If B12 = 1000, C12 = 1200 and D12 = 2 years, =LN(C12/B12)/D12 is approximately 0.091161 per year (9.1161% on a percentage display). This is the annual continuously compounded rate consistent with the start/end ratio—not a claim that the observations followed that model.

Compare multiplicative changes

=LN(2) is about 0.693147; =LN(0.5) is about -0.693147. A doubling and a halving have equal magnitude with opposite signs on a log scale.

Recover an original positive input

For B13 = 8, =EXP(LN(B13)) is mathematically 8. Test with a tolerance in precision-sensitive work: Apple warns that inverse operations can differ slightly because of floating-point representation.

• Log of zero: LN(0) is outside the function’s positive-number domain; check for zeros before using LN.
• Negative growth ratio: If end/start is negative, a real natural logarithm is not defined. Review the underlying signs and decide whether a log model is suitable.
• Unexpected negative result: Natural logs are negative for positive inputs between 0 and 1; that is correct, not necessarily a function error.
• 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.

Microsoft Excel documents LN(number) for a positive real number. It matches the mathematical function Apple describes. Exact numerical parity under extreme inputs or different locale rules has not been checked with either app. Microsoft documents the Excel counterpart in its official LN 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
• LOG
• LOG10

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.