# Logarithms Lesson 6 Episode 2 (Teachers)

### Exploring

Josh and Arobindo consider another student’s equation that is meant to describe the mold growth over two consecutive time periods. They decide the student has written an incorrect equation and propose a new equation. They explain why the two logarithmic expressions in their equation are equivalent.

### Episode Supports

Students’ Conceptual Challenges

The prompt from a fictional student provides opportunities for Josh and Arobindo, and your students, to examine the product rule for logarithms. Marcus’s equation exhibits a common error in reasoning with logarithms, that adding logarithms means we add their arguments. Some students might need time to think about Marcus’s claim. Encourage them to analyze it within the moldy pizza context, and to utilize a number line like Josh and Arobindo do.

Focus Questions

For use in a classroom, pause the video and ask these questions:

1. [Pause the video at 0:55] Do you agree or disagree with Marcus that log35 + log311 = log316? Why or why not?
2. [Pause the video at 3:03] The students have used logarithms to indicate elapsed time in the moldy pizza context. What does log35 and log311 mean in this context? Where do you see each of these expressions in the diagram that Arobindo and Josh have created?

Supporting Dialogue

Consider pausing the video at 1:46 and ask your students to discuss why Arobindo and Josh agree with only the left side of Marcus’s equation. What about that expression makes sense in this context? How might you change the equation to make it true?