# LogTen

## LogTen(x)

The base-10 logarithm of «x». This the the value *y* such that *10^y = x*.

Unless complex numbers are enabled, the parameter «x» must be must be non-negative or a warning will result. If Show Result Warnings is off, or the warning is ignored, the result is NaN.

When complex numbers are enabled, negative «x» values result in a result that is a complex number.

## Library

Math functions

## Examples

`LogTen(0) → -INF`

`LogTen(0.01) → -2`

`LogTen(1) → 0`

`LogTen(1K) → 3`

`LogTen(729)/LogTen(9) → 3`

## Complex numbers

When «x» is negative or complex, the result of LogTen(x) is a complex number. If you want LogTen to return a complex number for a negative parameter, you must set the system variable EnableComplexNumbers to 1, otherwise a warning is issued with a result of NaN. To set EnableComplexNumbers, see enabling complex numbers.

A complex number can be written in polar form as [math]\displaystyle{ r e^{\theta j} }[/math]. Thus, [math]\displaystyle{ \log x = \log r + {\theta\over{\log(10)}} j }[/math]. In other words, the real part of the result is the log magnitude, and the imaginary part is proportional to phasor angle, where [math]\displaystyle{ \theta }[/math] is written here as if in radians.

`LogTen(-1) → 1.364j { When EnableComplexNumbers is 1 }`

`LogTen(1000j) → 3+0.682j`

## See Also

- Ln(X) : The natural logarithm
- ProductLog
- Exp(x)
- Complex Numbers

Enable comment auto-refresher