Solution 1.3:6e - Revision history

Tek at 14:57, 22 September 2008

2008-09-22T14:57:31Z

←Older revision		Revision as of 14:57, 22 September 2008
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-	Both	+	Both 125 and 625 can be written as powers of 5,
-	~~<math>~~125~~</math>~~	+
-	and	+
-	~~<math>~~625~~</math>~~	+
-	can be written as powers of	+
-	~~<math>~~5~~</math>~~,	+

-		+	{{Displayed math\|\|<math>\begin{align}
-	<math>\begin{align}	+	125 &= 5\cdot 5 = 5\cdot 5\cdot 5 = 5^{3},\\[5pt]
-	& 125=5\~~centerdot~~ 5=5\~~centerdot~~ 5\~~centerdot~~ 5=5^{3} \\	+	625 &= 5\cdot 125 = 5\cdot 5^{3} = 5^{4},
-	& \\	+	\end{align}</math>}}
-	~~& 625~~=5\~~centerdot~~ 125=5\~~centerdot~~ 5^{3}=5^{4} \\	+
-	~~& \\~~	+
-	\end{align}</math>	+

	and this means that		and this means that

		+	{{Displayed math\|\|<math>\begin{align}
		+	125^{\frac{1}{2}} &= \bigl(5^{3}\bigr)^{\frac{1}{2}} = 5^{3\cdot\frac{1}{2}} = 5^{\frac{3}{2}},\\[5pt]
		+	625 &= \bigl(5^{4}\bigr)^{\frac{1}{3}} = 5^{4\cdot\frac{1}{3}} = 5^{\frac{4}{3}}\,\textrm{.}
		+	\end{align}</math>}}

-	~~<math>\begin{align}~~	+	From this, we see that <math>125^{\frac{1}{2}} > 625^{\frac{1}{3}}</math>, since the exponent 3/2 is bigger than 4/3 and the base 5 is bigger than 1.
-	~~& 125^{\frac{1}{2}}=\left( 5^{3} \right)^{\frac{1}{2}}=5^{3\centerdot \frac{1}{2}}=5^{\frac{3}{2}} \\~~	+
-	~~& \\~~	+
-	~~& 625=\left( 5^{4} \right)^{\frac{1}{3}}=5^{4\centerdot \frac{1}{3}}=5^{\frac{4}{3}} \\~~	+
-	~~\end{align}</math>~~	+
-		+
-		+
-	From this, we see that	+
-	<math>125^{\frac{1}{2}}>625^{\frac{1}{3}}</math>, since the exponent	+
-	~~<math>{~~3}/{2~~}\;</math>~~	+
-	is bigger than	+
-	~~<math>{~~4}/{3~~}\;</math>~~	+
-	and the base	+
-	~~<math>~~5~~</math>~~	+
-	is bigger than	+
-	~~<math>~~1~~</math>~~.	+

Ian at 12:59, 15 September 2008

2008-09-15T12:59:52Z

←Older revision		Revision as of 12:59, 15 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	Both
-	<~~center~~> ~~[[Image:1_3_6e.gif]]~~ </~~center~~>	+	<math>125</math>
-	{{~~NAVCONTENT_STOP~~}}	+	and
		+	<math>625</math>
		+	can be written as powers of
		+	<math>5</math>,
		+
		+
		+	<math>\begin{align}
		+	& 125=5\centerdot 5=5\centerdot 5\centerdot 5=5^{3} \\
		+	& \\
		+	& 625=5\centerdot 125=5\centerdot 5^{3}=5^{4} \\
		+	& \\
		+	\end{align}</math>
		+
		+	and this means that
		+
		+
		+	<math>\begin{align}
		+	& 125^{\frac{1}{2}}=\left( 5^{3} \right)^{\frac{1}{2}}=5^{3\centerdot \frac{1}{2}}=5^{\frac{3}{2}} \\
		+	& \\
		+	& 625=\left( 5^{4} \right)^{\frac{1}{3}}=5^{4\centerdot \frac{1}{3}}=5^{\frac{4}{3}} \\
		+	\end{align}</math>
		+
		+
		+	From this, we see that
		+	<math>125^{\frac{1}{2}}>625^{\frac{1}{3}}</math>, since the exponent
		+	<math>{3}/{2}\;</math>
		+	is bigger than
		+	<math>{4}/{3}\;</math>
		+	and the base
		+	<math>5</math>
		+	is bigger than
		+	<math>1</math>.

Tekbot: Lösning 1.3:6e moved to Solution 1.3:6e: Robot: moved page

2008-09-09T08:29:43Z

Lösning 1.3:6e moved to Solution 1.3:6e: Robot: moved page

←Older revision

Revision as of 08:29, 9 September 2008

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

2008-08-21T06:31:59Z

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

←Older revision		Revision as of 06:31, 21 August 2008
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2008-03-26T15:21:24Z

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