Logarithms and Non-Linear Data
Example 19
- First we rearrange \(P=aR^n\).
- \(\log P=\log(aR^n)\)
- Use the multiplication law: \(\log P=\log a+\log R^n\)
- Use the other law: \(\log P=\log a+n\log R\)
- Rearrange into \(y=mx+c\) form: \(\log P= n\log R+\log a\)
- Now we have to estimate \(a\) and \(n\).
- \(a\) is where the line on the graph intercepts the y axis. This means that \(a=6.2\).
- \(n\) is the gradient on the graph, therefore \(n=-0.67\) on here.