Purpose
Return value
Syntax
=LOG10(number)
- number - The positive number for which you want the base-10 logarithm.
Using the LOG10 function
LOG10 returns the base-10 logarithm of a number. In simple terms, it answers the question: “10 raised to what power gives me this number?” The table below shows how LOG10 works and how it is related to raising 10 to a specific power:
| Number | LOG10 | Because |
|---|---|---|
| 1000 | 3 | 10³ = 1000 |
| 100 | 2 | 10² = 100 |
| 10 | 1 | 10¹ = 10 |
| 1 | 0 | 10⁰ = 1 |
| 0.1 | -1 | 10⁻¹ = 0.1 |
| 0.01 | -2 | 10⁻² = 0.01 |
For numbers that aren’t exact powers of 10, LOG10 will return get decimals:
| Number | LOG10 |
|---|---|
| 50 | 1.699 |
| 3697 | 3.568 |
| 0.3697 | -0.432 |
To use Excel’s LOG10 function, just supply a number:
=LOG10(1000) // returns 3
=LOG10(100) // returns 2
=LOG10(10) // returns 1
=LOG10(1) // returns 0
=LOG10(0.1) // returns -1
=LOG10(0.01) // returns -2
Purpose
Return value
Syntax
=MDETERM(array)
- array - A square array of numbers only.
Using the MDETERM function
The MDETERM function returns the matrix determinant of a given array , which must be a square matrix containing numbers only, and no empty values. In mathematics, the matrix determinant is a scalar value (single value) that is a function of the entries in a square matrix. The determinant is a special number that can help characterize some properties of the matrix. For example, if the determinant is zero, the matrix will not have an inverse.
The MDETERM function takes just one argument, array , which can be provided as a range or an array constant . Array must be a square matrix with the same numbers of rows and columns.
Examples
To get the matrix determinant for the 2 x 2 array shown in B7:C8, the formula in E7 is:
=MDETERM(B7:C8) // returns -1
The equivalent formula with an array constant is:
=MDETERM({4,3;3,2}) // returns -1
To get the matrix determinant for the 3 x 3 array shown in I7:K9, the formula in M7 is:
=MDETERM(I7:K9) // returns 1
The equivalent formula with an array constant is:
=MDETERM({1,0,5;2,1,6;3,4,0}) // returns 1
Notes
- The array argument must be a square matrix with an equal number of rows and columns
- The array argument can be provided as a range or array constant like {4,3;3,2}
- Empty cells or text in array will cause MDETERM to return a #VALUE! error
- MDETERM returns a #VALUE! if array does not have an equal number of rows and columns
