Difference between revisions of "Manuals/calci/LN"
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*The Natural Logarithm is denoted by <math>ln(x)</math> or <math>log e(x)</math>. | *The Natural Logarithm is denoted by <math>ln(x)</math> or <math>log e(x)</math>. | ||
*where <math>x</math> is the Positive real number. | *where <math>x</math> is the Positive real number. | ||
| − | *The <math>ln(x)</math> is the inverse function of the exponential function <math>e^ln(x)=x</math> if <math>x>0</math>. | + | *The <math>ln(x)</math> is the inverse function of the exponential function <math>e^{ln(x)}=x</math> if <math>x>0</math>. |
*<math>ln(e^x)=x</math> | *<math>ln(e^x)=x</math> | ||
Revision as of 23:46, 15 December 2013
LN(n)
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} is the positive real number.
Description
- This function gives the Natural Logarithm of a number.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LN} is the logarithm in which the base is the irrational number Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e} (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e} = 2.71828...).
- For example, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ln_10 = loge_10 \approx 2.30258}
- Also called Napierian logarithm.
- The constant Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e} is called Euler's number.
- The Natural Logarithm is denoted by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ln(x)} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle log e(x)} .
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is the Positive real number.
- The Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ln(x)} is the inverse function of the exponential function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e^{ln(x)}=x} if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x>0} .
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ln(e^x)=x}
Examples
- =LN(15) = 2.708050201
- =LN(8.3) = 2.116255515
- =LN(1) = 0
- =LN(0) = INFINITY
- =LN(-20) = NAN
- =LN(exp(5)) = 5
- =EXP(LN(7)) = 7