LOGARITHM

Logarithm : If a  is a positive real number , other than 1 and a^m = x, then we write : m = log_ax and we say that the value of log x to base a is m .

Logarithm contains 2 parts :                                                                                                                         1. Characteristic : The integral part of the logarithm of a number is called its characteristic. 

 2. Mantissa:  The decimal part of the logarithm of a number is known as its mantissa

PROPERTIES 

1. log_a(xy)=log_a x  + log_a y 

2. log_a(x/Y)= log_a x -  log_a y

3. log_x x = 1

 4. log_a 1 = 0

 5. log_a(x^p) = p (log_a x)

  6. log_ax =  1/( log_x a)

  7. log_ax =  log x / log a

   8. a ^log_a x =  x 

   9. x^log _a y  = y ^log _ax

  10. log _a^q x^p = (p/q)  log_ax