From 2ac2db6ea1256eb6cc5bf785c8aade1f43a2fc05 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Thu, 25 Jan 2024 10:20:02 -0700 Subject: [PATCH] vault backup: 2024-01-25 10:20:02 --- education/math/Logarithms.md | 16 +++++++++++++++- 1 file changed, 15 insertions(+), 1 deletion(-) diff --git a/education/math/Logarithms.md b/education/math/Logarithms.md index 997c1ef..c9c594f 100644 --- a/education/math/Logarithms.md +++ b/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: -$$ log_3 sqrt(x) = \frac{1}{2}*log_3x $$ \ No newline at end of file +$$ log_3 sqrt(x) = \frac{1}{2}*log_3x $$ +## 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 |