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education/math/Logarithms.md

@@ -35,4 +35,18 @@ $$ log_5 y = 2 $$$$log_5(yz) = log_5 y + log_5 z $$$$ 2 + 3 = 5 $$
 Exponents can be moved to the front of a logarithm
 $$ log_3 x^5 = 5*log_3 x $$
 Roots are just the inverse, so:
-$$ log_3 sqrt(x) = \frac{1}{2}*log_3x $$
+$$ log_3 sqrt(x) = \frac{1}{2}*log_3x $$
+## Change of base
+$$ log_b x = \frac{\log x}{\log b} = \frac{\ln x}{\ln b} $$
+The above are all equivalent because the ratios are the same
+
+
+### The compound interest formula
+$$ A= Pe^{rt} $$
+
+| Value | Description |
+| ---- | ---- |
+| $A$ | Ending amount |
+| $P$ or $A_0$ | Starting amount |
+| $r$ or $k$ | Rate (a %) |
+| $t$ | The amount of times interest is compounded |