This task may be best used with a class who could evaluate log expressions and solve equations using them, so as to ensure there is some familiarity with the basic ideas. The task can be a lead in to looking at logarithmic graphs.  In experience when asked what is a log many pupils respond with ” the graph”, which may demonstrate a lack of understanding.  

This task is designed to help learners make associations between different representations of logarithms.  Written explicitly as a log statement, written as an exponential expression and also as a table of values for the graph of log base2.  

Some nice follow up tasks would be for the following table to be completed.  

The first task is looking at “nice” values on the logarithmic curve, this one then looks at how a small subset of those values look in comparison to their nearby values.  Pupils could be encouraged to write exponential and log expressions for these values too.  

Information from both tables can be combined to plot the graph.

Credit:  @chrismcgrane84