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education/math/Logarithms.md

@@ -5,9 +5,20 @@ Pronounced log *base* a, this function is used to figure out what exponent you n
 
 $log_ab = c$ can be rewritten as $a^c = b$.
 
-$$ 5^{log_5^(x+2)}=x+2 $$
+
+$$ 5^{log_5^{(x+2)}}=x+2 $$
 By default, $log$ refers to $log_{10}$. $ln$ is shorthand for $log_e$. 
 
 $$ \sqrt{x} = x^{1/2} $$
 To get the reciprocal of a value, change the sign of the exponent.
-$$ x = 
+$$ x^{-1} = \frac{1}{x} $$
+## Domain
+There are 3 places you need to worry about domain. 
+- You can't divide by 0
+- You can't take the square root of a negative without complex numbers
+- You cannot take the $log$ of a zero, or a negative number.
+	- There's no way to raise a number to an exponent and have it equal zero, or be a negative number.
+	- This can be used to help solve inequalities, because you know an equation that's wrapped in a logarithm must be $> 0$.
+
+## Adding logarithms
+$$ log(x+2)