Algebra Cheat Sheet - Algebra Cheat Sheet Basic Properties...

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For a complete set of online Algebra notes visit http://tutorial.math.lamar.edu . © 2005 Paul Dawkins Algebra Cheat Sheet Basic Properties & Facts Arithmetic Operations () ,0 ba b ab ac a b c a cc a aa a c b b cb c b c a c ad bc a c ad bc b d bd b d bd ab ba ab a b cd dc c c c a ab ac ad b bca c ab c d ⎛⎞ += + = ⎜⎟ ⎝⎠ == +− −= −− + + + =+ = Exponent Properties 1 1 0 1 1, 0 11 n m mm n n m nm n m nn m n n n n n n n n a a a a a ab a b bb b a a = ⎛⎞ ⎛⎞ = = ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ Properties of Radicals 1 , if is odd , if is even n n n n m m n n a b ab b b aan = = Properties of Inequalities If then and If and 0 then and If and 0 then and acbc c a c c a c < +<+ −<− < >< < < <> > Properties of Absolute Value if 0 if 0 a = < 0 Triangle Inequality a a a ab a b ≥− = +≤ + Distance Formula If ( ) 1 , P x y = and 22 2 , P x y = are two points the distance between them is ( ) ( ) 12 2 1 2 1 , dPP x x y y =− + Complex Numbers ( ) ( ) ( ) 2 2 , 0 Complex Modulus Complex Conjugate ii a i a a a bi c di a c b d i i cd i ac bd i a bi c di ac bd ad bc i iab i a b i a b i ab i i = =≥ ++ + + + + = + + = + + = +
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For a complete set of online Algebra notes visit http://tutorial.math.lamar.edu . © 2005 Paul Dawkins Logarithms and Log Properties Definition log is equivalent to y b yx x b == Example 3 5 log 125 3 because 5 125 Special Logarithms 10 ln log natural log log log common log e xx = = where 2.718281828 e = Logarithm Properties () log log 1 log 1 0 log log log log log log log log log b bb x x b r b b b bx b x xr x xy x y x xy y = = = =+ ⎛⎞ =− ⎜⎟ ⎝⎠ The domain of log b x is 0 x >
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This note was uploaded on 04/20/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).

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Algebra Cheat Sheet - Algebra Cheat Sheet Basic Properties...

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