LN in Zoho Sheet: Natural Logarithms and Doubling Time

=LN(number)

The directly retrieved official Zoho LN function reference was checked on 2026-10-11. Its public article documents the function but does not provide a first-supported Zoho version or establish identical results across every historical web, mobile, Windows and macOS client. This guide does not assign an undocumented version number.

Download or import roots-logs-practice.csv from the review batch. Columns A–C contain a record ID, the input number and a descriptive label. Enter formulas into D. This shared dataset can be reused for SQRT, SQRTPI, EXP, LN and LOG10, but each function’s domain must be checked separately.

The expected values were calculated outside Zoho Sheet using Python’s math functions; they are not screenshots, copied Zoho results or a native engine validation. They are rounded mathematical expectations, so cell formatting may show fewer digits.

Step-by-step worksheet exercise

1. Import roots-logs-practice.csv at A1. Column B contains eight valid strictly positive inputs in B2:B9; B10 and B11 intentionally contain -9 and 0 for later data-quality checks.
2. Enter Natural log in D1 and =LN(B2) in D2. With input 0.25, expect approximately -1.386294361.
3. Fill D2 down through D9. Note LN(1) = 0, LN(2) ≈ 0.693147181, LN(4) ≈ 1.386294361 and LN(10) ≈ 2.302585093.
4. Check the sign pattern: values less than 1 give negative results; values greater than 1 give positive results. This is an important sanity check before accepting a log-transformed imported dataset.
5. For the official Zoho example =LN(3.4), the documented result is 1.223775432. It is separate from this CSV but helps confirm that Zoho supports decimal inputs.
6. Do not fill into B10 or B11 and treat any resulting error as a surprise: LN(-9) and LN(0) lack real-number values. The native error token for these two specific expressions was not executed in this run.

Advanced: calculate doubling time for continuous growth

With a positive rate constant r, a continuously growing amount has model N(t)=N0×EXP(r×t). Solve 2×N0=N0×EXP(r×t) to get t = LN(2)/r. For r = 0.08 per year:

=LN(2)/0.08

The independently calculated doubling time is approximately 8.664339757 years. If the cell B2 holds a rate 8 instead of 0.08, the formula will be off by a factor of 100. This derivation assumes a constant, continuously compounded rate; do not apply it unchanged to annually compounded returns, changing growth rates or irregular time intervals.

You can also derive a continuous log growth rate from starting amount E2 and ending amount F2, observed across T periods in G2:

=LN(F2/E2)/G2

This is valid as a real logarithm only when E2>0, F2>0 and G2≠0. It gives an average continuously compounded log rate per period, not an ordinary percentage change. For an increase from 100 to 110 over one year, LN(110/100) ≈ 0.095310180. The arithmetic return is 10%, but the corresponding continuous log rate is approximately 9.531%; these are distinct definitions.

As an independent identity check, =EXP(LN(10)) should be numerically close to 10. Prefer a tolerance test for machine arithmetic rather than equality of full display strings.

• Zero and negatives: LN is defined for positive real inputs only. The official page lists generic spreadsheet errors but does not explicitly document which code a native Zoho session emits for LN(0) or LN(-9); record those as native-validation cases.
• Values below 1: A negative LN result is mathematically correct; an input such as 0.25 gives approximately -1.38629. Do not take ABS merely to make the result appear positive.
• Base confusion: LN uses base e, not base 10. For base-10 order of magnitude, use LOG10; for a custom base, check the separate LOG documentation.
• Division before LN: In LN(F2/E2), an input zero in E2 causes a division problem, even if F2 itself is positive.
• Tiny positives: Results can be large in magnitude and negative as the input approaches zero. This is not necessarily a software malfunction.
• Dates/units: Taking a logarithm directly of a date serial, a labelled unit or a physical quantity with no suitable reference ratio may be mathematically meaningless for an applied model.
• Text and historical versions: The public reference does not document every text coercion rule or a first-supported Zoho build.

Zoho’s function help pages list several common spreadsheet errors generically, including #N/A!; that is not proof that each error occurs for this specific arithmetic operation. Where the official function page gives a more specific domain error, the guide describes it above. For other domains, only a native Zoho test can confirm the exact engine response.

Microsoft’s Excel LN documentation also specifies a positive real-number input and identifies EXP as the inverse. This is a directly verified definition comparison; it does not establish identical error strings, conversion of imported text, rounding or treatment of overflow in Zoho Sheet. Google Sheets and spreadsheet programs may support the same name, but no native Google test was performed here. When translating rate formulas, preserve the underlying compounding model and input units; changing LN to LOG10 changes the numerical answer even where both functions exist.

• Zoho Sheet — function documentation

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

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