082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

2.4 Review of some common engineering functions and techniques 93
Y
2.5
x y Y=logy
−3 0.003 −2.54
−2 0.020 −1.69
−1 0.143 −0.85
0 1 0
1 7 0.85
2 49 1.69
3 343 2.54
–3 –2 –1 1 2 3 x
–2.5
Figure2.34
Alog--linear plotofy = 7 x producesa
straightline graph.
Example2.17 Considery =x 7 for 1 x10. Plot a log--log graph of thisfunction.
Solution We have
and so
y=x 7
logy = log(x 7 ) = 7logx
We plot logy against logx in Figure 2.35 for a log--log plot. PuttingY = logy and
X = logx we haveY = 7X which isastraightlinethrough the originwith gradient 7.
x y X=logx Y=logy
1 1 0 0
2 128 0.301 2.107
3 2187 0.477 3.340
4 16384 0.602 4.214
5 78125 0.699 4.893
6 279936 0.778 5.447
7 823543 0.845 5.916
8 2097152 0.903 6.322
9 4782969 0.954 6.680
10 10000000 1 7
Y
7
1 X
Figure2.35
A log--logplotofy =x 7
produces astraightline graph.
Examples 2.16 and 2.17 illustrate the following general points:
Alog--linear plot ofy =a x produces a straightlinewith a gradient of loga.
Alog--log plot ofy =x n produces a straightlinewith a gradient ofn.