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	<title>Woshka&#039;s Experiences &#187; Mathematics</title>
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		<title>Even Roots of Roots Numbers</title>
		<link>http://woshka.com/blog/mathematics/even-roots-of-roots-numbers.html</link>
		<comments>http://woshka.com/blog/mathematics/even-roots-of-roots-numbers.html#comments</comments>
		<pubDate>Sat, 02 Jan 2010 03:15:01 +0000</pubDate>
		<dc:creator>voshka</dc:creator>
				<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://blog.woshka.com/?p=57</guid>
		<description><![CDATA[Here x 2  &#62; 0 for all real numbers x. Therefore the equation  x 2 = b only has solutions x when b &#62; 0, that is only when b is non-negative.  Defining
b½ =sqrt(b)
as the nonnegative real solution of  x 2 = b works only  if b is positive. ...]]></description>
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		<slash:comments>0</slash:comments>
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		<title>Properties of Exponentials</title>
		<link>http://woshka.com/blog/mathematics/properties-of-exponentials.html</link>
		<comments>http://woshka.com/blog/mathematics/properties-of-exponentials.html#comments</comments>
		<pubDate>Sat, 02 Jan 2010 03:13:42 +0000</pubDate>
		<dc:creator>voshka</dc:creator>
				<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://blog.woshka.com/?p=55</guid>
		<description><![CDATA[Now (a x)y = exp(y ln(a x )) =   exp(y x ln(a )) =  a yx = a xy Therefore
(a x)y =  a xy (Exponential of an exponential)
Now a xay =  exp(x ln(a)) · exp(y ln(a) = exp(x ln(a)+y ln(a)) = exp( (x +y )ln(a) ) = a x+y Therefore  ...]]></description>
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		<slash:comments>0</slash:comments>
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		<title>Exponentials of Real Numbers a x  = exp( x ln(a))</title>
		<link>http://woshka.com/blog/mathematics/exponentials-of-real-numbers-a-x-exp-x-lna.html</link>
		<comments>http://woshka.com/blog/mathematics/exponentials-of-real-numbers-a-x-exp-x-lna.html#comments</comments>
		<pubDate>Sat, 02 Jan 2010 03:11:18 +0000</pubDate>
		<dc:creator>voshka</dc:creator>
				<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://blog.woshka.com/?p=50</guid>
		<description><![CDATA[For x = m/n and a &#62; 0,  a x = a m/n = exp( (m/n) ln(a)) = exp( x ln(a)). This suggests putting a x  = exp( x ln(a)) for x irrational.  Then
a x  = exp( x ln(a)) for all real x for a   &#62; ...]]></description>
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		<title>Natural Logarithms and Exponentials &#8211; Roots and Powers</title>
		<link>http://woshka.com/blog/mathematics/natural-logarithms-and-exponentials-roots-and-powers.html</link>
		<comments>http://woshka.com/blog/mathematics/natural-logarithms-and-exponentials-roots-and-powers.html#comments</comments>
		<pubDate>Sat, 02 Jan 2010 03:08:36 +0000</pubDate>
		<dc:creator>voshka</dc:creator>
				<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://blog.woshka.com/?p=46</guid>
		<description><![CDATA[today I was preparing myself for the math exam that I have for the next week
I learned the exponentional exp(x) and logarithms ln(x) functions
Uniqueness (or 1 to 1) Property:
If a &#62; 0, b&#62; 0 and  ln(a) = ln(b) then a = b..
Inversion Properties

ln(exp(x)) = x for all real x
exp(ln(x)) = ...]]></description>
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		<slash:comments>13</slash:comments>
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