Lösung 3.3:3d

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We write the argument of <math>\log_{3}</math> as a power of 3,
We write the argument of <math>\log_{3}</math> as a power of 3,
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{{Displayed math||<math>9\cdot 3^{1/3} = 3^2\cdot 3^{1/3} = 3^{2+1/3} = 3^{7/3}\,,</math>}}
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{{Abgesetzte Formel||<math>9\cdot 3^{1/3} = 3^2\cdot 3^{1/3} = 3^{2+1/3} = 3^{7/3}\,,</math>}}
and then simplify the expression with the logarithm laws
and then simplify the expression with the logarithm laws
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{{Displayed math||<math>\log _3 (9\cdot 3^{1/3}) = \log_3 3^{7/3} = \frac{7}{3}\cdot \log_3 3 = \frac{7}{3}\cdot 1 = \frac{7}{3}\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>\log _3 (9\cdot 3^{1/3}) = \log_3 3^{7/3} = \frac{7}{3}\cdot \log_3 3 = \frac{7}{3}\cdot 1 = \frac{7}{3}\,\textrm{.}</math>}}

Version vom 08:43, 22. Okt. 2008

We write the argument of \displaystyle \log_{3} as a power of 3,

\displaystyle 9\cdot 3^{1/3} = 3^2\cdot 3^{1/3} = 3^{2+1/3} = 3^{7/3}\,,

and then simplify the expression with the logarithm laws

\displaystyle \log _3 (9\cdot 3^{1/3}) = \log_3 3^{7/3} = \frac{7}{3}\cdot \log_3 3 = \frac{7}{3}\cdot 1 = \frac{7}{3}\,\textrm{.}
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_3.3:3d“