Lösung 3.3:6b
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
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The logarithm <math>\lg 46</math> satisfies the relation | The logarithm <math>\lg 46</math> satisfies the relation | ||
| - | {{ | + | {{Abgesetzte Formel||<math>10^{\lg 46} = 46</math>}} |
and taking the natural logarithm of both sides, we obtain | and taking the natural logarithm of both sides, we obtain | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\ln 10^{\lg 46 } = \ln 46\,\textrm{.}</math>}} |
If we use the logarithm law, <math>\lg a^b = b\cdot\lg a</math>, on the left-hand side, the equality becomes | If we use the logarithm law, <math>\lg a^b = b\cdot\lg a</math>, on the left-hand side, the equality becomes | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\lg 46\cdot\ln 10 = \ln 46\,\textrm{.}</math>}} |
This shows that | This shows that | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\lg 46 = \frac{\ln 46}{\ln 10} = \frac{3\textrm{.}828641\,\ldots}{2\textrm{.}302585\,\ldots} = 1\textrm{.}6627578\,\ldots</math>}} |
and the answer is 1.663. | and the answer is 1.663. | ||
Version vom 08:45, 22. Okt. 2008
The logarithm \displaystyle \lg 46 satisfies the relation
| \displaystyle 10^{\lg 46} = 46 |
and taking the natural logarithm of both sides, we obtain
| \displaystyle \ln 10^{\lg 46 } = \ln 46\,\textrm{.} |
If we use the logarithm law, \displaystyle \lg a^b = b\cdot\lg a, on the left-hand side, the equality becomes
| \displaystyle \lg 46\cdot\ln 10 = \ln 46\,\textrm{.} |
This shows that
| \displaystyle \lg 46 = \frac{\ln 46}{\ln 10} = \frac{3\textrm{.}828641\,\ldots}{2\textrm{.}302585\,\ldots} = 1\textrm{.}6627578\,\ldots |
and the answer is 1.663.
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