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Display information for equation id:math.220135.40 on revision:220135

* Page found: Median (eq math.220135.40)

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TeX (original user input):

 var[ \log( t_a / t_b ) ] = var[ \log( t_a ) ] + var[ \log( t_b )] - 2r ( var[ \log( t_a ) ] var[ \log( t_b ) ] )^{0.5}

TeX (checked):

var[\log(t_{a}/t_{b})]=var[\log(t_{a})]+var[\log(t_{b})]-2r(var[\log(t_{a})]var[\log(t_{b})])^{0.5}

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v times a times r times left-bracket log left-parenthesis t Subscript a Baseline slash t Subscript b Baseline right-parenthesis right-bracket equals v times a times r times left-bracket log left-parenthesis t Subscript a Baseline right-parenthesis right-bracket plus v times a times r times left-bracket log left-parenthesis t Subscript b Baseline right-parenthesis right-bracket minus 2 times r times left-parenthesis v times a times r times left-bracket log left-parenthesis t Subscript a Baseline right-parenthesis right-bracket times v times a times r times left-bracket log left-parenthesis t Subscript b Baseline right-parenthesis right-bracket right-parenthesis Superscript 0.5

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: v*a*r*[log(t[a]/ t[b])]= v*a*r*[log(t[a])]+ v*a*r*[log(t[b])]- 2*r*(v*a*r*[log(t[a])]*v*a*r*[log(t[b])])^(0.5)

Information about the conversion process:

\log: Logarithm; Example: \log@@{z}

Will be translated to: log($0)

Translation Information: Without a given base, ln equals log.

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=log



Translation to Mathematica

In Mathematica: v*a*r*[Log[Subscript[t, a]/ Subscript[t, b]]]= v*a*r*[Log[Subscript[t, a]]]+ v*a*r*[Log[Subscript[t, b]]]- 2*r*(v*a*r*[Log[Subscript[t, a]]]*v*a*r*[Log[Subscript[t, b]]])^(0.5)

Information about the conversion process:

\log: Logarithm; Example: \log@@{z}

Will be translated to: Log[$0]

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Mathematica: https://reference.wolfram.com/language/ref/Log.html



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