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