Lösung 3.3:3c

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First, we rewrite the number 0.125 as a fraction which we also simplify
First, we rewrite the number 0.125 as a fraction which we also simplify
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{{Displayed math||<math>0\textrm{.}125 = \frac{125}{1000} = \frac{5\cdot 25}{10^3} = \frac{5\cdot 5\cdot 5}{(2\cdot 5)^3} = \frac{1}{2^3} = 2^{-3}\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>0\textrm{.}125 = \frac{125}{1000} = \frac{5\cdot 25}{10^3} = \frac{5\cdot 5\cdot 5}{(2\cdot 5)^3} = \frac{1}{2^3} = 2^{-3}\,\textrm{.}</math>}}
Because 0.125 was expressed as a power of 2, the logarithm can be calculated in full
Because 0.125 was expressed as a power of 2, the logarithm can be calculated in full
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{{Displayed math||<math>\log_2 0\textrm{.}125 = \log_2 2^{-3} = (-3)\cdot\log_2 2 = (-3)\cdot 1 = -3\,\textrm{.}</math>}}
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{{Abgesetzte Formel||<math>\log_2 0\textrm{.}125 = \log_2 2^{-3} = (-3)\cdot\log_2 2 = (-3)\cdot 1 = -3\,\textrm{.}</math>}}

Version vom 08:42, 22. Okt. 2008

First, we rewrite the number 0.125 as a fraction which we also simplify

\displaystyle 0\textrm{.}125 = \frac{125}{1000} = \frac{5\cdot 25}{10^3} = \frac{5\cdot 5\cdot 5}{(2\cdot 5)^3} = \frac{1}{2^3} = 2^{-3}\,\textrm{.}

Because 0.125 was expressed as a power of 2, the logarithm can be calculated in full

\displaystyle \log_2 0\textrm{.}125 = \log_2 2^{-3} = (-3)\cdot\log_2 2 = (-3)\cdot 1 = -3\,\textrm{.}
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_3.3:3c“