THINK AND DISCUSS

let us observe the scale factor in the graph of y=2 On X-axis (Refer Ratio - proportion) If 10 places = 1 unit 20 places =2 units 40 places=4 units, then Can you imagine the corresponding value on X-axis, with reference to the 5 on Y-axis?

We rewrite the above table as follows



Observe the graph y=2' in the light of our definition of logarithm



i.e y-cordinate of any point on the curve is the xth power of 2, and x-coordinate of any point on the curve is the logarithm of y- coordinate to the base 2.

Let us consider one more example:

If 10^y= 25 then it can be represented as y = log₁₀ 25 or y= log 25, Logarithms of a number to the base 10 are also called common logarithms. In this case,

we generally omit the base i.e. log₁₀ 25 is also written as log 25.

In general, a and N are positive real numbers such that a +1 we define log N =x= x² =N.



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