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education/math/Logarithms.md

@@ -22,4 +22,15 @@ There are 3 places you need to worry about domain.
 
 ## Adding logarithms
 $$ log(x+2) + log(2x-3) $$
-With the above example, you can find the domain of each function separately, then find the overlap of valid numbers.
+With the above example, you can find the domain of each function separately, then find the overlap of valid numbers.
+
+
+# Expanding logarithms
+$$ log_b(x*y) = log_b x + log_b y $$
+$$log_b(\frac{x}{y}) = log_b x - log_b y $$
+
+Example Problem:
+$$ log_5 z = 3 $$
+$$ log_5 y = 2 $$$$log_5(yz) = log_5 y + log_5 z $$$$ 2 + 3 = 5 $$
+Exponents can be moved to the front of a logarithm
+$$ log_3 x^5 = 5*log_3 x $$