Logarithm

Logarithm

Keywords: logarithm

The base a logarithm of number b is the power to which number a must be raised in order to get number b

a l o g a b = b
( l o g 2 8 = 3     2 3 = 8 )
a = 10 ,   l o g 10 x = l g x
a = e = 2.718 ,   l o g e x = l n x

Important logarithm identities

l o g a a = 1
l o g a 1 = 0
l o g a a n = n

Logarithmic identities

l o g a ( x y ) = l o g a x + l o g a y
l o g a ( x y ) = l o g a x l o g a y
l o g a x n = n l o g a x

Changing the base of a logarithm

l o g a x = l o g b x l o g b a
l o g a b · l o g b a = 1
a l o g b c = c l o g b a
l o g a x = l o g a n x n