Solution 3.3:5e

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Current revision (07:33, 2 October 2008) (edit) (undo)
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The argument of ln can be written as
The argument of ln can be written as
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{{Displayed math||<math>\frac{1}{e^{2}} = e^{-2}</math>}}
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<math>\frac{1}{e^{2}}=e^{-2}</math>
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and with the logarithm law, <math>\ln a^{b} = b\ln a</math>, we obtain
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{{Displayed math||<math>\ln \frac{1}{e^{2}} = \ln e^{-2} = (-2)\cdot\ln e = (-2)\cdot 1 = -2\,\textrm{.}</math>}}
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and with the logarithm law,
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<math>\lg a^{b}=b\lg a</math>, we obtain
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<math>\ln \frac{1}{e^{2}}=\ln e^{-2}=\left( -2 \right)\centerdot \ln e=\left( -2 \right)\centerdot 1=-2</math>
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Current revision

The argument of ln can be written as

\displaystyle \frac{1}{e^{2}} = e^{-2}

and with the logarithm law, \displaystyle \ln a^{b} = b\ln a, we obtain

\displaystyle \ln \frac{1}{e^{2}} = \ln e^{-2} = (-2)\cdot\ln e = (-2)\cdot 1 = -2\,\textrm{.}
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