Transforming Graphs using Logs (Cambridge (CIE) AS Maths): Revision Note

Transforming graphs using logs

What are logarithmic axes?

• For graphs that increases or decreases exponentially

  • it can very difficult to read specific values from the scales on the axes

• Taking ln of both sides allows the equation to be rearranged into the form “y = mx + c”

• Plotting ln y against t produces a straight line

  • The -axis is a logarithmic axis

• Note the second graph has ln y on the y-axis

  • Log graphs have at least one logarithmic axis

• Reading a value for ln y at t = 20 is easier than reading the value for y

• Logarithmic axes are used where a wide range of numbers can occur

  • it makes numbers smaller and easier to deal with

  • a curve can be turned into a straight line

How do I transform graphs into straight lines using logs?

• Exponential models are of the form

  • y=Ab^kx (growth)

  • y=Ab^-kx (decay)

• To use a model to make predictions the values of A, b and k are needed

• A, b and k will usually be estimated from observed data values

  • A may be known exactly, as it is a starting/initial value

• Estimating from a straight line graph is easier than from a curve