In this clip the students are solving an equation in which the exponent is unknown.
Introduction to Logarithms, Clip 1, 3:21
In this clip the teacher has made the decision she does not want them to use their calculator but rather estimate what the exponents should be. This can help keep from logarithms becoming a procedural routine.
She waits until the end of the exercise to give them the notation. She is trying to push the fact that the output of logarithms is an exponent. Taking this approach forces them to think about what exponent is necessary before they ever use logarithmic notation.
