Page 35 - Mathematics Class - XII

ACTIVITY 3.2

OBJECTIVE
To establish a relationship between common logarithm (to the base 10) and natural logarithm (to the base e) of
the number x.

MATERIAL REQUIRED

Y Cardboard/Drawing board
Y White sheet
Y Graph paper

Y Pencil
Y Scale

Y Log tables or calculator (graphic/scientific)

PRE-REQUISITE KNOWLEDGE
1. Knowledge of logarithm to the base 10 i.e., common logarithm.

2. Knowledge of logarithm to the base e i.e., natural logarithm.

PROCEDURE
1. On the drawing board, fix a thick paper sheet of convenient size with adhesive. And fix a graph paper on it.
2. On the graph sheet, take two perpendicular lines XOX′ and YOY′, depicting the coordinate axes.

3. Find some ordered pairs satisfying the function y = log x, using log tables / calculator and draw the graph
10
of the function on the graph paper (see Fig. (a)).
4. Similarly, draw the graph of y′ = log x on the same graph paper as shown in Fig. (a) (using log tables/
e
calculator).

DEMONSTRATION

1. Take any point on the positive direction of x-axis, and note its x-coordinate.
2. For this value of x, find the value of y-coordinates for both the graphs of y = log x and y′ = log x by
e
10
actual measurement, using a scale, and record them as y and y′ respectively.

x 1 2 3 4 5 6 7 8 9 10

log 1 log 2 log 3 log 4 log 5 log 6 log 7 log 8 log 9 log 10
10
10
10
10
10
10
10
10
10
10
y = log x
10
0 0.3010 0.4771 0.6021 0.6990 0.7782 0.8451 0.9031 0.9542 1
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