Difference between revisions of "LogTen"
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The base-10 logarithm of «x». This the the value ''y'' such that ''10^y = x''. | The base-10 logarithm of «x». This the the value ''y'' such that ''10^y = x''. | ||
| − | «x» must be non-negative or a warning will result. If [[Preferences|Show Result Warnings]] is off, or the warning is ignored, the result is [[NaN]]. | + | Unless [[EnableComplexNumbers|complex numbers are enabled]], the parameter «x» must be must be non-negative or a warning will result. If [[Preferences|Show Result Warnings]] is off, or the warning is ignored, the result is [[NaN]]. |
| + | |||
| + | When [[EnableComplexNumbers|complex numbers are enabled]], negative «x» values result in a result that is a complex number. | ||
= Library = | = Library = | ||
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:LogTen(1K) → 3 | :LogTen(1K) → 3 | ||
:LogTen(729) / LogTen(9) → 3 | :LogTen(729) / LogTen(9) → 3 | ||
| + | |||
| + | = Complex numbers = | ||
| + | |||
| + | When «x» is negative or complex, the result of <code>[[LogTen]](x)</code> 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 [[EnableComplexNumbers|enabling complex numbers]]. | ||
| + | |||
| + | A complex number can be written in polar form as <math>r e^{\theta j}</math>. Thus, <math>\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>\theta</math> is written here as if in radians. | ||
| + | |||
| + | :<code>LogTen(-1)</code>→1.364j '' Note: when [[EnableComplexNumbers]] is 1'' | ||
| + | :<code>LogTen(1000j)</code>→3+0.682j | ||
= See Also = | = See Also = | ||
* [[Ln]](X) : The natural logarithm. | * [[Ln]](X) : The natural logarithm. | ||
| + | * [[Exp]](x) | ||
| + | * [[Complex Numbers]] | ||
| + | |||
| + | <comments /> | ||
Revision as of 19:39, 15 April 2013
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 Note: when EnableComplexNumbers is 1LogTen(1000j)→3+0.682j
See Also
- Ln(X) : The natural logarithm.
- Exp(x)
- Complex Numbers
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