RUME 27
2025
Alexandria, Virginia
All My Work is Right, Why Didn’t I Get the Right Answer? When Logarithmic Identities Fail
Page: 1161
When learning about logarithms and solving logarithmic equations, students often misapply logarithmic identities. In some cases, misapplying an identity leads to the deletion of solutions or the introduction of extraneous solutions. This results from applying an identity without first checking that all logarithms in that identity are defined on the same domain. In this preliminary work, we examined 14 websites that College Algebra students might use when learning how to solve equations using logarithms, looking for mentions of the domains of definition whenever identities were stated or applied. Of the 11 websites that stated a logarithmic identity, only 4 mentioned domains of definition. Of the 11 websites that showed an example logarithmic identity application, zero mentioned domains of definition. We hypothesize that this lack of emphasis on domains of definition in teaching and learning logarithmic identities may lead to confusion when working with logarithms and in mathematics as a whole.