# Logarithms Lesson 5 Episode 3 (Teachers)

### Exploring

Arobindo and Josh interpret the expression log3 (10)as the time at which the pizza slice had a certain amount of mold

### Episode Supports

Students’ Conceptual Challenges

Early in the video [0:55], the instructor asks what is happening to the mold over the period from 1 million hours to 1 million + x hours. Arobindo initially says it’s “bizillioning” out, indicating it is growing very large. On the one hand, he is correct in that the amount of mold is incredibly large. However, it is not clear if he understands that the amount of mold is also increasing by a factor of 10. This challenge might be present with your students. It is important that they understand and remember that for exponential functions, the function grows by equal factors over equal time periods, no matter how large or small these quantities are.

Focus Questions

For use in a classroom, pause the video and ask this question:

[Pause the video at 1:04] What do you make of Arobindo’s claim that the amount of mold is “bizillioning” out? How else can you describe how the mold is growing from 1 million hours to 1 million + x hours, where x = log310?

Supporting Dialogue

Ask students to discuss how Arobindo and Josh connect the logarithmic expression log310 to the time it takes for mold to increase by a factor of 10. Ask them to discuss how they utilize the number line to reason with the expression.