Lösung 3.3:3h
Aus Online Mathematik Brückenkurs 1
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Version vom 14:36, 22. Okt. 2008
Because \displaystyle a^{2}\sqrt{a} = a^{2}a^{1/2} = a^{2+1/2} = a^{5/2}, the logarithm law, \displaystyle b\lg a = \lg a^b, gives that
| \displaystyle \log_{a} \bigl(a^{2}\sqrt{a}\,\bigr) = \log_{a}a^{5/2} = \frac{5}{2}\cdot\log_{a}a = \frac{5}{2}\cdot 1 = \frac{5}{2}\,, |
where we have used that \displaystyle \log_{a}a = 1\,.
Note: In this exercise, we assume, implicitly, that \displaystyle a > 0 and \displaystyle a\ne 1\,.
