Definition:

 

A logarithm is the exponential function b to the y power equals x written in the form log base b of x equals y

 

Common logarithm (base 10):

 

log base 10 of x equals common log x

 

Natural logarithm (base e):

 

log base e of x equals natural log x

 

Properties of logarithms:

 

log base b of one equals zeronatural log of one equals zero

log base b of b equals onenatural log of e equals one

log base b of b to the x power equals xnatural log of e to the x power equals x

b rasied to the log base b of x equals xe raised to the natural log of x equals x

 

Laws of logarithms:

 

log base b of the product xy equals log base b of x plus log base b of y

log base b of the quotient x over y equals log base b of x minus log base b of y

log base b of x to the y power equals y times the log base b of x

 

Change of base formula:

 

log base b of x equals log base a of x divided by log base a of b where b and x are greater than zero