# Logarithms Lesson 5

### Comparing Interpretations of Logarithms

The students continue to explore the two interpretations of logarithms in the moldy pizza context that they had found before, one as the hour at which the slice has a certain amount of mold and the other as the amount of time it takes for the mold to increase by a certain factor. They interpret several logarithmic expressions in both ways.

##### Episode 1: Making Sense

The students use the definition of a logarithm to say what log3 (10) means generally. They find its value and discuss why that value makes sense, given the definition.

##### Episode 2: Exploring

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

##### Episode 3: Exploring

Josh and Arobindo interpret the expression log3 (10) as the time it takes the mold on the pizza slice to increase by a certain factor.

##### Episode 4: Repeating Your Reasoning

The students explore a different moldy food–a peanut butter sandwich. The mold on the sandwich increases by a factor of 4 each hour. The students write a logarithmic expression that describes when the sandwich will have 200 grams of mold.

##### Episode 5: Repeating Your Reasoning

Josh and Arobindo write a logarithmic expression that describes that amount of time it takes the mold on the peanut butter sandwich to increase by a factor of 20.