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 a^y =x. And we write log_a(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= log_a(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.