Documentation/Calc Functions/LOG
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Function name:
LOG
Category:
Mathematical
Summary:
Calculates the logarithm to a specified base of a positive real number.
Syntax:
LOG(Number [; Base])
Returns:
Returns a real number that is the logarithm to the specified base of the given number.
Arguments:
Number is a positive real number, or a reference to a cell containing that number, that is the value for which the logarithm is to be calculated.
Base is a positive real number, or a reference to a cell containing that number, that is the base to be used for calculating the logarithm of Number. If Base is omitted, LOG uses a default value of 10.
- If either Number or Base is non-numeric, then LOG reports a #VALUE! error.
- If either Number or Base is less than or equal to 0, then LOG reports an invalid argument error (Err:502).
- If Base is equal to 1, then LOG reports an invalid argument error (Err:502).
Additional details:
- The following change of base formula may be used to determine a logarithm for any base:
[math]\displaystyle{ \text{log}_b(x)~=~\frac{\text{log}_d(x)}{\text{log}_d(b)} }[/math]
- This formula is valid for positive real numbers x, b, and d, such that neither b nor d is equal to 1.
- The figure below illustrates the LOG function when Base is set to 2 (known as binary logarithms).
- See LN for the corresponding illustration when Base is set to the mathematical constant e (natural logarithms).
- See LOG10 for the corresponding illustration when Base is set to 10 (common logarithms).
Examples:
| Formula | Description | Returns |
|---|---|---|
| =LOG(3.5; 5) | Here the function returns the logarithm to base 5 of 3.5. | 0.778385397048775 |
| =LOG(0.5; 4) | Here the function returns the logarithm to base 4 of 0.5. | −0.5 |
| =LOG(D1; D2) where cells D1 and D2 contain the numbers 1 and 9 respectively. | Here the function returns the logarithm to base 9 of 1 (the logarithm of 1 is always zero, for any base). | 0 |
| =LOG(2.5; 5.7) | Here the function returns the logarithm to base 5.7 of 2.5. | 0.526462820777384 |
| =LOG(POWER(7; 34); 7) | Here the function returns the logarithm to base 7 of 7 raised to the power of 34, which is 34. | 34 |
| =POWER(13; LOG(789, 13)) | Here the function returns 13 to the power of the logarithm to base 13 of 789, which is 789. | 788.999999999999 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
LOG