Solution 3.3:5a

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The notation ln is used for the logarithm with the natural base
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<center> [[Image:3_3_5a.gif]] </center>
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<math>e=\text{2}.\text{7182818}...,</math>
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and we therefore have that
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<math>\text{ln }e=\text{1}</math>, which together with the logarithm law,
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<math>b\lg a=\lg a^{b}</math>, gives that
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<math>\ln e^{3}+\ln e^{2}=3\centerdot \ln e+2\centerdot \ln e=3\centerdot 1+2\centerdot 1=5</math>

Revision as of 08:19, 26 September 2008

The notation ln is used for the logarithm with the natural base \displaystyle e=\text{2}.\text{7182818}...,

and we therefore have that \displaystyle \text{ln }e=\text{1}, which together with the logarithm law, \displaystyle b\lg a=\lg a^{b}, gives that


\displaystyle \ln e^{3}+\ln e^{2}=3\centerdot \ln e+2\centerdot \ln e=3\centerdot 1+2\centerdot 1=5

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