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student:mathematics:logarithms [2018/08/26 14:33] – created bernstdhstudent:mathematics:logarithms [2018/08/26 15:08] (current) bernstdh
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-===== Mathematical Foundations: Logarithms =====+===== Logarithms =====
  
  
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   - logu/v=logulogv   - logu/v=logulogv
   - loguk=klogu for u>0   - loguk=klogu for u>0
-  - logbu=(logba)(logau) for u>0 +  - logbu=(logba)(logau) for u>0 \\ To prove this result let  u=ap (so that  p=logau).  Then: \\ logbu=logbap=plogba=(logba)(logau)
-To prove this result let  u=ap (so that  p=logau).  Then: +
-logbu=logbap=plogba=(logba)(logau)+
   - logbu=1logub   - logbu=1logub
-  - Combining the previous two rules yields the following "change of base rule": +  - Combining the previous two rules yields the following "change of base rule":\\ logbu=logaulogab for u>0 
-\\ +  - ddulogbu=1(ulnb) where ln denotes the natural logarithm  (i.e., loge).
-logbu=logaulogab for u>0 +
-  - ddulogbu=1(ulnb) where ln denotes the natural logarithm  i.e., loge).+