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Transforming Exponential Equations

Any equation of the formwhereandare constants, andandare variables, can be transformed into a linear equation by taking logs.

Ifthen

Using the logarithm lawwithandand natural logs gives

Using the logarithm law(again using natural logs) with the second term on the right hand side gives

This is equation of a straight line, with x plotted against ln y .

Straight line graphs are desirable because theintercept and gradient are easy to find and this allows the constants of the original exponential equation to be found.

The– intercept of the straight line graph above is 1.1

soto 1 decimal place.

The gradient of the graph isto 2 decimal places soto two decimal places.

Thento within the limits of our graph.

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