Tuesday, September 2, 2008

Logarithm-3

USEFUL FORMULAE OF LOGARITHM


  1. loga(mn)=logam + logan
  2. loga(m/n) = logam - logan
  3. logamn = nlogam
  4. logbm = logam/logab
  5. (logab)(logba) = 1
  6.   
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Monday, September 1, 2008

LOGARITHM-2

In my last article (Logarithm-1) I explained to you that what does it mean to take the logarithm of a number x to some base a. I explained there that when we take the logarithm of x to base a, we try to find out that to what power we must raise a to get x. In this sense if we have decided the value of a then for every value of x we will get a value y such that ay =x. And we write loga(x)=y.

For example let us take a=10.

Then following table illustrates the changing values of y with the changing values of x.

X

y= log10(x)

Explanation

0.01

-2

10-2=0.01

0.1

-1

10-1=0.1

1

0

100=1

10

1

101=10

100

2

102=100

1000

3

103=1000


So we see that for every value of x , log10(x) gives an unique value of y. This kind of arrangement in mathematics is known as FUNCTION. Thus we can treat LOGARITHM as a function.

Therefore, now onwards we will treat y= loga(x) as a FUNCTION.

Rules for the values of base a, argument x and dependent variable y:

a ε (0,+∞) - {1}. Base a can take all positive values except 1.

x ε (0, +∞) ; Domain of logarithmic function.

y ε (- ∞,+∞) ; Range of logarithmic function.