LOGARITHMS

 

 

Exponential Form:  x = by

Example:

8 = 23

 

Logarithmic Form:  y = logb x

 

Example:

 

3 = log2 8

 b > 0

 

 

Common Logarithms:  Logarithms with base 10.         b = 10

 

Logarithm of a negative number is not defined.  Example:  log2 (-8) is undefined.

 

 

Basic Properties of Logarithms:

 

logb 1 = 0

 

Example:

Log3 1 = 0

 

30 = 1

logb b = 1

 

Example:

Log3 3 = 1

 

31 = 3

logb bx = x

 

Example:

Log3 34 = 4

 

34 = 34

 

blogbx = x

 

Example:

3log34 = 4

 

Log3 4 = log3 4

 

 

Properties of Logarithms:

 

Logaxy = loga x + loga y

Example:

Log4 (2*32) = Log464 = log4 2 + log4 32

= loga x - loga y

 

 

Example:

= log3 81 log3 27 = 4 3 = 1

 

Logaxr = rlogax

Example:

Log482 = 2log48

 

 

 

Change of Base Formulas: