Lösung 3.3:4c - Versionsgeschichte

Markus.bez: Sprache und Formulierung

2009-06-12T10:59:22Z

Sprache und Formulierung

← Nächstältere Version		Version vom 10:59, 12. Jun. 2009
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-	Alle Argumente können wie Potenzen ~~mit der~~ Basis 3 geschrieben werden	+	Alle Argumente können wie Potenzen zur Basis 3 geschrieben werden:

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}
-	27^{\frac{1}{3}} &= \bigl(3^3\bigr)^{\frac{1}{3}} = 3^{3\cdot\frac{1}{3}} = 3^1 = 3\,,\\[5pt]	+	27^{\frac{1}{3}} &= \bigl(3^3\bigr)^{\frac{1}{3}} = 3^{3\cdot\frac{1}{3}} = 3^1 = 3\,\text{und}\\[5pt]
-	\frac{1}{9} &= \frac{1}{3^2} = 3^{-2}\,,\\	+	\frac{1}{9} &= \frac{1}{3^2} = 3^{-2}\,.\\
	\end{align}</math>}}		\end{align}</math>}}

Martin um 20:38, 26. Mär. 2009

2009-03-26T20:38:15Z

← Nächstältere Version		Version vom 20:38, 26. Mär. 2009
Zeile 1:		Zeile 1:
-	~~All three arguments of the logarithm can be written as powers of~~ 3,	+	Alle Argumente können wie Potenzen mit der Basis 3 geschrieben werden

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}
Zeile 6:		Zeile 6:
	\end{align}</math>}}		\end{align}</math>}}

-	~~and it is therefore appropriate to use base 3 when simplifying using the logarithms, even if we have the base 10-logarithm, lg,~~	+	Wir vereinfachen den Ausdruck mit Hilfe des Logarithmengesetzes

	{{Abgesetzte Formel\|\|<math>\begin{align}		{{Abgesetzte Formel\|\|<math>\begin{align}
Zeile 16:		Zeile 16:
	\end{align}</math>}}		\end{align}</math>}}

-	~~This expression cannot be simplified any further~~.	+	Dieser Ausdruck kann nicht weiter vereinfacht werden.

Tekbot: hat „Solution 3.3:4c“ nach „Lösung 3.3:4c“ verschoben: Robot: moved page

2008-10-22T14:37:05Z

hat „Solution 3.3:4c“ nach „Lösung 3.3:4c“ verschoben: Robot: moved page

← Nächstältere Version

Version vom 14:37, 22. Okt. 2008

Tekbot: Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

2008-10-22T08:44:08Z

Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)

← Nächstältere Version		Version vom 08:44, 22. Okt. 2008
Zeile 1:		Zeile 1:
	All three arguments of the logarithm can be written as powers of 3,		All three arguments of the logarithm can be written as powers of 3,

-	{{~~Displayed math~~\|\|<math>\begin{align}	+	{{Abgesetzte Formel\|\|<math>\begin{align}
	27^{\frac{1}{3}} &= \bigl(3^3\bigr)^{\frac{1}{3}} = 3^{3\cdot\frac{1}{3}} = 3^1 = 3\,,\\[5pt]		27^{\frac{1}{3}} &= \bigl(3^3\bigr)^{\frac{1}{3}} = 3^{3\cdot\frac{1}{3}} = 3^1 = 3\,,\\[5pt]
	\frac{1}{9} &= \frac{1}{3^2} = 3^{-2}\,,\\		\frac{1}{9} &= \frac{1}{3^2} = 3^{-2}\,,\\
Zeile 8:		Zeile 8:
	and it is therefore appropriate to use base 3 when simplifying using the logarithms, even if we have the base 10-logarithm, lg,		and it is therefore appropriate to use base 3 when simplifying using the logarithms, even if we have the base 10-logarithm, lg,

-	{{~~Displayed math~~\|\|<math>\begin{align}	+	{{Abgesetzte Formel\|\|<math>\begin{align}
	\lg 27^{\frac{1}{3}} + \frac{\lg 3}{2} + \lg \frac{1}{9}		\lg 27^{\frac{1}{3}} + \frac{\lg 3}{2} + \lg \frac{1}{9}
	&= \lg 3 + \frac{1}{2}\lg 3 + \lg 3^{-2}\\[5pt]		&= \lg 3 + \frac{1}{2}\lg 3 + \lg 3^{-2}\\[5pt]

Tek um 07:16, 2. Okt. 2008

2008-10-02T07:16:14Z

← Nächstältere Version		Version vom 07:16, 2. Okt. 2008
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-	All three arguments of the logarithm can be written as powers of	+	All three arguments of the logarithm can be written as powers of 3,
-	~~<math>\text{~~3~~}</math>~~,	+

-	<math>\begin{align}	+	{{Displayed math\|\|<math>\begin{align}
-	& 27^{\frac{1}{3}}=\~~left~~( 3^{3} \~~right~~)^{\frac{1}{3}}=3^{3\~~centerdot~~ \frac{1}{3}}=3^{1}=3, \\	+	27^{\frac{1}{3}} &= \bigl(3^3\bigr)^{\frac{1}{3}} = 3^{3\cdot\frac{1}{3}} = 3^1 = 3\,,\\[5pt]
-	& \frac{1}{9}=\frac{1}{3^{2}}=3^{-2} \\	+	\frac{1}{9} &= \frac{1}{3^2} = 3^{-2}\,,\\
-	\end{align}</math>	+	\end{align}</math>}}

		+	and it is therefore appropriate to use base 3 when simplifying using the logarithms, even if we have the base 10-logarithm, lg,

-		+	{{Displayed math\|\|<math>\begin{align}
-	~~and it is therefore appropriate to use base~~	+	\lg 27^{\frac{1}{3}} + \frac{\lg 3}{2} + \lg \frac{1}{9}
-	~~<math>\text~~{~~3}</math>~~	+	&= \lg 3 + \frac{1}{2}\lg 3 + \lg 3^{-2}\\[5pt]
-	~~when simplifying using the logarithms, even if we have the base~~	+	&= \lg 3 + \frac{1}{2}\lg 3 + (-2)\cdot\lg 3\\[5pt]
-	~~<math>\text~~{~~1}0</~~math>	+	&= \Bigl(1+\frac{1}{2}-2\Bigr)\lg 3\\[5pt]
-	~~logarithm, lg,~~	+	&= -\frac{1}{2}\lg 3\,\textrm{.}
-		+	\end{align}</math>}}
-		+
-	<math>\begin{align}	+
-	& \lg 27^{\frac{1}{3}}+\frac{\lg 3}{2}+\lg \frac{1}{9}=\lg 3+\frac{1}{2}\lg 3+\lg 3^{-2} \\	+
-	& =\lg 3+\frac{1}{2}\lg 3+~~\left~~( -2 ~~\right~~)\~~centerdot~~ \lg 3 \\	+
-	& =\~~left~~( 1+\frac{1}{2}-2 \~~right~~)\lg 3=-\frac{1}{2}\lg 3 \\	+
-	\end{align}</math>	+
-		+

	This expression cannot be simplified any further.		This expression cannot be simplified any further.

Ian um 14:58, 25. Sep. 2008

2008-09-25T14:58:24Z

← Nächstältere Version		Version vom 14:58, 25. Sep. 2008
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-	{{~~NAVCONTENT_START~~}}	+	All three arguments of the logarithm can be written as powers of
-	<~~center~~> ~~[[Image:3_3_4c.gif]]~~ </~~center~~>	+	<math>\text{3}</math>,
-	{{~~NAVCONTENT_STOP~~}}	+
		+	<math>\begin{align}
		+	& 27^{\frac{1}{3}}=\left( 3^{3} \right)^{\frac{1}{3}}=3^{3\centerdot \frac{1}{3}}=3^{1}=3, \\
		+	& \frac{1}{9}=\frac{1}{3^{2}}=3^{-2} \\
		+	\end{align}</math>
		+
		+
		+
		+	and it is therefore appropriate to use base
		+	<math>\text{3}</math>
		+	when simplifying using the logarithms, even if we have the base
		+	<math>\text{1}0</math>
		+	logarithm, lg,
		+
		+
		+	<math>\begin{align}
		+	& \lg 27^{\frac{1}{3}}+\frac{\lg 3}{2}+\lg \frac{1}{9}=\lg 3+\frac{1}{2}\lg 3+\lg 3^{-2} \\
		+	& =\lg 3+\frac{1}{2}\lg 3+\left( -2 \right)\centerdot \lg 3 \\
		+	& =\left( 1+\frac{1}{2}-2 \right)\lg 3=-\frac{1}{2}\lg 3 \\
		+	\end{align}</math>
		+
		+
		+	This expression cannot be simplified any further.

Tekbot: Lösning 3.3:4c moved to Solution 3.3:4c: Robot: moved page

2008-09-09T09:26:43Z

Lösning 3.3:4c moved to Solution 3.3:4c: Robot: moved page

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Version vom 09:26, 9. Sep. 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-08-21T07:00:29Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

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2008-04-02T09:50:31Z

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