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student:mathematics:logarithms [2018/08/26 14:34] – bernstdhstudent:mathematics:logarithms [2018/08/26 15:08] (current) – bernstdh
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-===== Mathematical Foundations: Logarithms =====+===== Logarithms =====
  
  
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   - \(\log_{b}u = \frac{1}{\log_{u}b}\)   - \(\log_{b}u = \frac{1}{\log_{u}b}\)
   - Combining the previous two rules yields the following "change of base rule":\\ \(\log_{b}u = \frac{\log_{a}u}{\log_{a}b} \mbox{ for }  u \gt 0\)   - Combining the previous two rules yields the following "change of base rule":\\ \(\log_{b}u = \frac{\log_{a}u}{\log_{a}b} \mbox{ for }  u \gt 0\)
-  - \( \frac{d}{du} \log_{b}u= \frac{1}{( u \ln b)}\) where \(\ln\) denotes the natural logarithm  i.e., \(\log_{e}\)).+  - \( \frac{d}{du} \log_{b}u= \frac{1}{( u \ln b)}\) where \(\ln\) denotes the natural logarithm  (i.e., \(\log_{e}\)).