In such situation, a new relation logarithm is introduced. Consider y = 2x we need the value ofx for which y becomes 5 from the facts that if x=1 then y=21=2,if x=2 then y=22=4,if x=3 then y=23=8, we observe that x lies between 2and3 we will now use the graph of y=2x to locate such as 'x' for which 2x=5.

Graph of Exponential 2x

 Let us draw the graph of y=2x For this we compute the value of 'y' by choosing some values for 'x'
x -3 -2 -1 0 1 2 3
y=2x 1/8 1/4 1/2 1 2 4 8
We plot the points and connect them with smooth curveNote that as x increase the value of y=2x.As x decreases the value of y=2x decreases very close to 0 but never attains the value 0. Let us think, if y=2x then for which value of x,y become 5?

We know that, in the graph Y- axis represents the value of 2xand X- axis represents the value of x. Locate the value of 5 on Y - axis, and represent it as a corresponding point "P" on Y- axis. Draw a line parallel to X- axis through P, which meets the graph at the point Q.

Now draw QR perpendicular to X - axis. Can we find the length of OR approximately from the graph? or where does it lie? Thus, we know that the x coordinate of the point R is the required value of x, for which 2x=5.

This value of x is called the logarithm of 5 to the base 2, written as log2 5.



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