LESSON 5: DEFINITION AND LAWS OF LOGARITHMS

Definition
The log of a number is the power to which the base must be raised to give that number.

Laws of logarithms

 * 1) The multiplication law
 * 2) The division law
 * 3) The power law

The multiplication law
Let logbM = x

and

logbN = y

or in index form

M = bx and

N =by Now

MN =bx x by and

MN =bx+y or in log form logbMN = x + y

The division law
Now M/N = bx/by and

M/N = b(x-y) or in log form

logbM/N = x-y

Hence

The power law
Now Mn = (bx)n and

Mn = bnx or in log form

The value of logb1
Let logb1 = x

then in index form 1 =bx

Hence logb1 = 0

therefore

The value of logbb
Let logbb = x

then in index form b = bx

Hence logbb = 1

Therefore

The value of logb0
Let logbo = x

then in index form 0 = bx

Hence logb0 = -infinity

Therefore

The value of logb(-N)
Let logb(-N) = x

then in index form -N = bx

Hence logb(-N) has no real value

Therefore

question
Find the value of x in each of the following

a. logx9 = 2

solution
in index form x2 = 9 and

x =&radic;9 therefore

x = 3 ans

b. log7x = 0

solution
in index form x = 70 therefore x = 1  ans

Malackt 15:49, 26 February 2007 (CET)