ABSTRACT
At the end of this chapter, you should be able to:
• understand logarithmic scales • understand log-log and log-linear graph paper • plot a graph of the form y = axn using log-log graph paper and determine constants ‘a’ and ‘n’ • plot a graph of the form y = abx using log-linear graph paper and determine constants ‘a’ and ‘b’ • plot a graph of the form y = aekx using log-linear graph paper and determine constants ‘a’ and ‘k’
Graph paper is available where the scale markings along the horizontal and vertical axes are proportional to the logarithms of the numbers. Such graph paper is called log-log graph paper. A logarithmic scale is shown in Fig. 30.1 where distance between, say 1 and 2, is proportional to lg 2-lg 1, i.e. 0.3010 of the total distance from 1 to 10. Similarly, the distance between 7 and 8 is proportional to lg 8-lg 7, i.e. 0.05799 of the total distance from 1 to
10. Thus the distance between markings progressively decreases as the numbers increase from 1 to 10. With log-log graph paper the scale markings are from 1 to 9, and this pattern can be repeated several times. The number of times the pattern of markings is repeated on an axis signifies the number of cycles. When the vertical axis has, say, 3 sets of values from 1 to 9, and
the horizontal axis has, say, 2 sets of values from 1 to 9, then this log-log graph paper is called ‘log 3 cycle × 2 cycle’ (see Fig. 30.2). Many different arrangements, are available ranging from ‘log 1 cycle×1 cycle’ through to ‘log 5 cycle×5 cycle’. To depict a set of values, say, from 0.4 to 161, on an axis of log-log graph paper, 4 cycles are required, from 0.1 to 1, 1 to 10, 10 to 100 and 100 to 1000.
