more work on ICB practice response

diff --git a/methods/stuff.md b/methods/stuff.md
index 93354091686509a8c414097a53e15cc572cd76f6..37878ddb3f7d8a682a864579eefb109801999438 100644 (file)
--- a/methods/stuff.md
+++ b/methods/stuff.md
@@ -1,4 +1,16 @@
-# Index laws
+---
+geometry: margin=2cm
+<!-- columns: 2 -->
+graphics: yes
+tables: yes
+author: Andrew Lorimer
+classoption: twocolumn
+header-includes: \pagenumbering{gobble}
+---
+
+# random methods shit
+
+## Index laws
 
 $a^m \times a^n = a^{m+n}$  
 $a^m \div a^n = a^{m-n}4$  
@@ -6,6 +18,19 @@ $(a^m)^n = a^{_mn}$
 $(ab)^m = a^m b^m$  
 ${({a \over b})}^m = {a^m \over b^m}$
 
-# Fractional indices
+## Fractional indices
+
+$^n\sqrt{x}=x^{1/n}$
+
+## Logarithms
+
+$$\log_b (x) = n \quad \operatorname{where} \hspace{0.5em} b^n=x$$
+
+## Using logs to solve index eq's
+
+Used for equations without common base exponent
+
+Or change base:  
+$$\log_b c = {{\log_a c} \over {\log_a b}}$$
 
-$^n\sqrt{x}=x^{1/n}$
\ No newline at end of file
+If $a<1, \quad \log_{b} a < 0$ (flip inequality operator)
\ No newline at end of file