How to use the LOG10 function
What is the LOG10 function?
The LOG10 function calculates the logarithm of a number using the base 10.
What is a logarithm?
In logarithms, the base is the number that is raised to a power to produce the desired output. It is the foundation of the logarithmic function.
What is a base?
In logarithms, the base is the number that is raised to a power to produce the desired output. It is the foundation of the logarithmic function.
For example, the logarithm log10(100):
- 10 is the base
- 100 is the input number
- 2 is the exponent that makes 10 return 100 because 102Â = 100
The most common bases are
- 10
- e (natural log), and
- 2 (for computers).
But any positive number besides 1 can be a base.
What is the definition of a logarithm with an base of 10?
For the base 10:
log10(x) = lim (n->infinity) (x^(1/n) - 1) * n / log10(e)
Where:
-
- 10 is the base
- x is the input number
- e is the mathematical constant (approximately 2.71828...)
This limit definition comes from Euler's Logarithm Definition, relating logs of any base b to the natural log ln(x).
What are the other logarithmic functions in Excel?
| Excel function | Description |
|---|---|
| LOG | Returns the logarithm with a given base. |
| LN | Returns the natural logarithm (base e) of a number |
| LOG10 | Returns the base-10 logarithm of a number |
| LOG2 | Returns the base-2 logarithm of a number |
The corresponding inverse functions for the logarithm functions in Excel:
| Logarithm | Power to |
|---|---|
| LOG | Arbitrary base, basex or POWER(number, power) |
| LN | EXP(number) |
| LOG10 | 10x or POWER(10,x) |
| LOG2 | 2x or POWER(2,x) |
Formula in cell C3:
Excel Function Syntax
LOG10(number)
Arguments
| number | Required. A value larger than 0 (zero) that you want to calculate the logarithm with base 10. |
Comments
The LOG10 function returns #NUM! error if number is equal to 0 (zero) or smaller.
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Functions in 'Math and trigonometry' category
The LOG10 function function is one of many functions in the 'Math and trigonometry' category.
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