Lösung 3.3:3g
Aus Online Mathematik Brückenkurs 1
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Version vom 14:35, 22. Okt. 2008
Using the logarithm law, \displaystyle \lg a-\lg b = \lg\frac{a}{b}\,, the expression can be calculated as
| \displaystyle \log_3 12 - \log_3 4 = \log_3\frac{12}{4} = \log _3 3 = 1\,\textrm{.} |
Another way is to write \displaystyle 12 = 3\cdot 4 and use the logarithm law, \displaystyle \lg (ab) = \lg a + \lg b\,,
| \displaystyle \begin{align}
\log _{3}12 - \log _{3}4 &= \log_{3}(3\cdot 4) - \log_{3} 4\\[5pt] &= \log_{3}3 + \log _{3}4 - \log _{3}4\\[5pt] &= \log _{3}3\\[5pt] &= 1\,\textrm{.} \end{align} |
