In this paper, we discuss three implementations of a task in which students were asked to generate examples of logarithm expressions equal to a given value. We situate the design of the task in variation theory and in research on learner generated examples, which describe learning as developing students' ways of seeing, particularly in regards to the dimensions of variation and the range of permissible change. The analysis of the three implementations reveals students' understanding of logarithms, as well as what is possible to learn given the task-as-implemented, or the enacted object of learning. We claim that using variation theory in task design can support students in developing important capabilities for reasoning about logarithms in powerful ways.