Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
student:mathematics:logarithms [2018/08/26 14:33] – bernstdh | student:mathematics:logarithms [2018/08/26 15:08] (current) – bernstdh | ||
---|---|---|---|
Line 1: | Line 1: | ||
- | ===== Mathematical Foundations: | + | ===== Logarithms ===== |
Line 27: | Line 27: | ||
- \(\log_{b}u = (\log_{b}a) (\log_{a}u) \mbox{ for } u \gt 0\) \\ To prove this result let \(u= a^{p}\) (so that \(p=\log_{a}u\)). | - \(\log_{b}u = (\log_{b}a) (\log_{a}u) \mbox{ for } u \gt 0\) \\ To prove this result let \(u= a^{p}\) (so that \(p=\log_{a}u\)). | ||
- \(\log_{b}u = \frac{1}{\log_{u}b}\) | - \(\log_{b}u = \frac{1}{\log_{u}b}\) | ||
- | - Combining the previous two rules yields the following " | + | - Combining the previous two rules yields the following " |
- | \\ | + | - \( \frac{d}{du} \log_{b}u= \frac{1}{( u \ln b)}\) where \(\ln\) denotes the natural logarithm |
- | \(\log_{b}u = \frac{\log_{a}u}{\log_{a}b} \mbox{ for } u \gt 0\) | + | |
- | - \( \frac{d}{du} \log_{b}u= \frac{1}{( u \ln b)}\) where \(\ln\) denotes the natural logarithm | + |