# Logarithms Lesson 5 Episode 1 (Teachers)

### 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 Supports

Students’ Conceptual Challenges

Although Josh and Arobindo seem to still be connecting logarithms to exponents, they initially seem unsure that 3log310 equals 10. Eventually, they talk through the meaning of logarithms and exponents and make this connection, but it isn’t automatic. Expect this to take some time for your students as well. The Focus Questions and Supporting Dialogue prompts can facilitate conversations that help your students make sense of this idea.

Focus Questions

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

1. [Pause the video at 0:35] What sense do you make of what Arobindo and Josh have written at the beginning of this episode: 3 log310 = ? and 3x. What does raising a base to a logarithm of that same base do?
2. [Pause the video at 2:07] Can you rephrase the conversation you just heard? What does it mean that log310 “is the exponent that makes 3x equal 10?”

Supporting Dialogue

After watching the video, ask your students to check in with each other. What does the expression 3log310 mean? Ask your students to tell a partner one thing they have learned about logarithms and one thing they are still working through or are confused by.