From f9bf9a8e88aa129ca3f559bd4e8aeeda87095a38 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Fri, 19 Jan 2024 09:19:11 -0700 Subject: [PATCH] vault backup: 2024-01-19 09:19:11 --- education/math/Logarithms.md | 15 +++++++++++++-- 1 file changed, 13 insertions(+), 2 deletions(-) diff --git a/education/math/Logarithms.md b/education/math/Logarithms.md index a656033..b42bfdd 100644 --- a/education/math/Logarithms.md +++ b/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. -$$ x = \ No newline at end of file +$$ 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) \ No newline at end of file