Linear Law - Linearisation Using Logarithms
Linear Law - Linearisation Using Logarithms
The table below shows experimental values of two variables \(x\) and \(y\) which are related by the equation \(y = ax^b\), where \(a\) and \(b\) are constants.
| \(x\) | \(1.5\) | \(2\) | \(2.5\) | \(3\) | \(4.5\) | \(6\) |
|---|---|---|---|---|---|---|
| \(y\) | \(45\) | \(25\) | \(15.8\) | \(11\) | \(5\) | \(2.6\) |
- Plot a straight line graph of \(\lg y\) against \(\lg x\).
- Use your graph to estimate the value of \(a\) and of \(b\).
- On the same diagram, draw the line representing the equation \(y = x^3\) and hence find the value of \(x\) for which \(x^{3-b} = a\).
Solution:
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Answer:(i) Log–log straight-line plot shown. (ii) \(a\approx100,b\approx-2\). (iii) \(x\approx2.51\).
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