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re
[methods] logarithm laws
author
Andrew Lorimer
<andrew@lorimer.id.au>
Tue, 5 Mar 2019 01:59:08 +0000
(12:59 +1100)
committer
Andrew Lorimer
<andrew@lorimer.id.au>
Tue, 5 Mar 2019 01:59:08 +0000
(12:59 +1100)
methods/stuff.md
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diff --git
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b/methods/stuff.md
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methods/stuff.md
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methods/stuff.md
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-40,4
+40,16
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If $a<1, \quad \log_{b} a < 0$ (flip inequality operator)
$e^x$ - natural exponential function
$e^x$ - natural exponential function
-$$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
\ No newline at end of file
+$$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
+
+## Logarithm laws
+
+$\log_a(mn) = \log_am + \log_an$
+$\log_a({m \over n}) = \log_am - \log_an$
+$\log_a(m^p) = p\log_am$
+$\log_a(m^{-1}) = -\log_am$
+$\log_a1 = 0$ and $\log_aa = 1$
+
+## Inverse functions
+
+Inverse of $f: \mathbb{R} \rightarrow \mathbb{R}, f(x)=a^x$ is $f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$