algebra fact sheet

Calculus I Algebra Fact Sheet Basic Algebra ( ) 2 2 2 2 a b a ab b + = + + ( ) 3 3 2 2 3 3 3 a b a ab ab b + = + + + ( )( ) 2 2 a b a b a b − = + − ( )( ) 2 2 a b a bi a bi + = + − ( ) ( ) 3 3 2 2 a b a b a ab b − = − + + ( ) ( ) 3 3 2 2 a b a b a ab b + = + − + a c ad bc b d bd ± ± = Rules of Exponents m n m n xx x + = m m n n x x x − = ( ) n m mn x x = / n mn m x x = 1 n n x x − = 1 x y y x − = ( ) 0 1 0 x x = ≠ Radicals 1/2 x x = 1/3 3 x x = Real Numbers xy x y = x x y y = Complex Numbers 1 i = − 2 1 i =− Logarithmic Functions log y b y x b x = ⇔ = ( ) log log log b b b mn m n = + log log log b b b m m n n = − log log n b b m n m = 1 log log b b x x =− log x b b x = log b x b x = Quadratic Formula/Solving 2 0 ax bx c + + = 2 4 2 b b ac x a − ± − = 2 x n x n = ⇔ =± Natural and Common Logarithms ( ) 10 log ln 2.71828 log log e x x e x x = ≈ = ln y y x e x = ⇔ = log 10 y y x x = ⇔ = ln x e x = ln 1 e = ln x e x = ln1 0 = log log ln log log log ln b a b x x x x a a a = = = Graphs of Exponentials and Logs www.TrigCheatSheet.com

Upload: bala1307

Post on 06-Nov-2015

6 views

Category:

Documents

4 download

Report

Download

Embed Size (px):

DESCRIPTION

MAth

TRANSCRIPT

Calculus I

Algebra Fact Sheet

Basic Algebra

( )2 2 22a b a ab b+ = + +

( )3 3 2 2 33 3a b a a b ab b+ = + + +

( )( )2 2a b a b a b = + ( )( )2 2a b a bi a bi+ = +

( )( )3 3 2 2a b a b a ab b = + + ( )( )3 3 2 2a b a b a ab b+ = + +

a c ad bcb d bd

=

Rules of Exponents m n m nx x x +=

mm n

n

x xx

=

( )nm mnx x= / nm n mx x=

1nnx x

=

1x yy x

=

( )0 1 0x x=

Radicals 1/2x x= 1/33 x x=

Real Numbers xy x y=

x xy y=

Complex Numbers 1i =

2 1i =

Logarithmic Functions

log yby x b x= =

( )log log logb b bmn m n= +

log log logb b bm m nn

=

log lognb bm n m= 1log logb b xx

=

log xb b x= logb xb x=

Quadratic Formula/Solving 2 0ax bx c+ + =

2 42

b b acxa

=

2x n x n= =

Natural and Common Logarithms

( )10

log ln 2.71828log log

e x x ex x=

=

ln yy x e x= = log 10yy x x= =

ln xe x= ln 1e = ln xe x= ln1 0=

log log lnloglog log ln

ba

b

x x xxa a a

= = =

Graphs of Exponentials and Logs

www.TrigCheatSheet.com