From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 5 Mar 2019 01:59:08 +0000 (+1100)
Subject: [methods] logarithm laws
X-Git-Tag: yr12~223
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/77db891721cf67f5118278e2571c653fb143e56f?ds=sidebyside

[methods] logarithm laws
---

diff --git a/methods/stuff.md b/methods/stuff.md
index 0424391..1cbb98b 100644
--- a/methods/stuff.md
+++ b/methods/stuff.md
@@ -40,4 +40,16 @@ If $a<1, \quad \log_{b} a < 0$ (flip inequality operator)
 $e^x$ - 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 $f^{-1}: \mathbb{R}^+ \rightarrow \mathbb{R}, f^{-1}=log_ax$