LOG in Zoho Sheet: Custom-Base Logarithms and Growth Models
Calculate custom-base logarithms in Zoho Sheet, read precise LOG syntax, and use step-by-step examples for doubling time and scale changes.
Verification status: Official documentation referenced; example outcomes independently reasoned or arithmetically checked where stated. Not executed in Zoho Sheet. How formula examples are checked
Zoho Sheet LOG: formula, examples and practical use
Quick answer: =LOG(8;2) returns 3, because 2 cubed is 8. =LOG(100) returns 2 because the optional base defaults to 10. LOG is useful when an analyst needs to answer “what exponent converts this base into that value?” rather than perform ordinary division or multiplication.
Unlike the common logarithm LOG10 and the natural logarithm LN, Zoho’s LOG accepts a configurable base. A logarithm is an exponent, not a ratio: for valid positive x and positive b other than 1, LOG(x;b)=y means b^y=x. For example, LOG(0.125;2) is -3 because two to the power -3 is one eighth; this negative logarithm is mathematically valid. Avoid confusing a negative result with a negative input, which is outside the real domain.
Exact documented syntax and arguments
=LOG(number; [base])
| Argument | Required | Official meaning and practical check |
|---|---|---|
number |
Yes | Positive real number to take the logarithm of. Zoho documents #NUM! for numbers ≤ 0. |
base |
No | Base to use; defaults to 10 when omitted. In real-number mathematics base must be positive and not 1. Zoho’s page does not specify an exact display/error outcome for every invalid base, so native tests are still needed. |
The directly checked Zoho LOG article uses the ; separator and gives =LOG(50;10) → 1.698970004. Its separately linked official catalogue entry may appear with an ambiguous article slug; use the resolved log-function link, not a guessed /articles/log URL.
Example workbook: values, bases, and expected answers
Import logarithms-practice.csv. It contains an input number in column B and a base in column C; column D is an explanation, not a formula result. Enter =LOG(B2;C2) in E2 and fill down. To compare common logarithms, enter =LOG(B2) in F2 for rows with valid positive B values. Excel-style comma separators are not the spelling shown in the checked Zoho article.
| Row | B: positive number | C: base | Formula in E | Independently expected |
|---|---|---|---|---|
| 2 | 0.125 | 2 | =LOG(B2;C2) |
-3 |
| 3 | 0.5 | 2 | =LOG(B3;C3) |
-1 |
| 4 | 1 | 10 | =LOG(B4;C4) |
0 |
| 5 | 2 | 2 | =LOG(B5;C5) |
1 |
| 6 | 8 | 2 | =LOG(B6;C6) |
3 |
| 7 | 10 | 10 | =LOG(B7;C7) |
1 |
| 8 | 32 | 2 | =LOG(B8;C8) |
5 |
| 9 | 50 | 10 | =LOG(B9;C9) |
1.698970004 |
| 10 | 100 | 10 | =LOG(B10;C10) |
2 |
| 11 | 1000 | 10 | =LOG(B11;C11) |
3 |
- Check the numerical type of each B/C cell and confirm B is strictly positive.
- In E2 type
=LOG(B2;C2); observe that the formula refers to the row’s base. - Fill the formula down for the complete data range; do not accidentally lock the first base with
$C$2. - In F2 type
=LOG(B2)to see the decimal-base interpretation. Compare the two columns only where the row’s base differs from 10. - For a hand-check, raise the chosen base to the independently expected exponent. For example
=POWER(2;3)corresponds to=LOG(8;2)=3.
Important: the values in the table are mathematical expectations from Python, not results viewed in Zoho Sheet. Do not treat formatting to nine decimals as a guarantee of Zoho precision.
Advanced example 1: how many compounding periods to double?
Suppose a balance grows by 5% per period. A balance after n periods is initial_balance * 1.05^n. Set initial and target balances to 100 and 200. The exact required number of periods satisfies 1.05^n=2, so type =LOG(2;1.05) and expect approximately 14.206699082. If each period must be completed before a balance threshold is achieved, =CEILING(LOG(2;1.05);1) yields 15 whole periods; this use of CEILING is for positive values and integer increments. Separate the fractional analytic duration from the operational full-period count.
For an arbitrary start value in B2, target in C2, and periodic growth fraction in D2, use =LOG(C2/B2;1+D2). Guard it: B2 and C2 must be positive, 1+D2 must be positive and not equal to 1. Negative growth can still be modeled mathematically when 0<1+D2<1, but the direction and threshold interpretation change. This example does not evaluate the expression inside a Zoho account.
Advanced example 2: change of logarithm base
When a function supports only natural logarithms in a different system, the identity log_b(x)=ln(x)/ln(b) offers a cross-check. Type =LN(32)/LN(2) and compare with =LOG(32;2); both are mathematically 5. Use this identity to audit rounding differences, not to assume both formulas share identical error handling. If b=1, the denominator LN(1) is zero, so the conversion cannot produce a finite real answer.
Errors, edge cases, and troubleshooting
| Issue | Cause and remedy |
|---|---|
#NUM! for LOG(0;2) or a negative number |
Zoho expressly documents a nonpositive first argument as a numeric-domain error. Validate input before taking the logarithm. |
| Base set to 1, 0, or a negative number | Invalid for ordinary real-valued logarithms; the checked Zoho page does not state the precise native error for every such base. Flag the row and test natively. |
#VALUE! |
An input has an invalid type according to Zoho’s general error description. Check text imported as a number, spaces, and locale decimal marks. |
#NAME! |
Check the exact function spelling LOG and the list separator supported by your current editor. |
| Unexpected minus sign | LOG(0.5;2)=-1 is correct. The input is positive but less than 1. |
LOG(100) differs from LOG(100;2) |
Omitting the base means base 10, not base e or base 2. |
| Different rounding from Python or Excel | Do not compare unrounded floating-point outputs for equality; round the displayed value for a human report, retaining full precision for downstream calculations. |
When not to use LOG: do not use it to calculate a simple percentage change ((new-old)/old), a linear daily average, or a digit count in a text identifier. The logarithm model applies when multiplicative scaling is actually part of the task.
Verified cross-software reference for this function
Microsoft Excel LOG reference explicitly documents LOG(number, [base]) and its default base of 10; these are aligned with the checked Zoho concepts, but punctuation and error coercion should be verified in the target file.
How this compares with Excel and Google Sheets
Microsoft Excel documents related functions with comma-delimited examples in an English-language setting, while the checked Zoho Sheet help uses semicolons where multiple arguments occur. Spreadsheet separators can be affected by application and locale settings; do not blindly paste a formula across products without checking the target editor. Shared mathematics does not prove that all data-type coercion, numerical precision, errors, locales, or desktop/mobile support are identical. Where a relevant Microsoft help page is linked below, it establishes only the Excel behaviour specifically described there. Google Sheets may offer the same named function, but that name alone is not a native Zoho compatibility test.
Official reference and verification
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.