EL5 Tweaks

[siwelwerd]

Remark 5.5.1 Using "Then" makes it sound like the three displayed equations follow from what comes before. Activity 5.5.2(b) I don't see this property explicitly in Section 5.3. Also, a missing \ on the second log. These seem to be repeated in the following activity. Definition 5.5.11 Where does this formula come from?

[tdegeorge]

@kathypinzon See Drew's comment about for Activity 5.5.2(b). Did you want to put something in your section that states the same thing somewhere?

[tdegeorge]

For Definition 5.5.11 - As a group, we debated putting in the change of base formula because not everyone uses it. We ultimately decided to put it in in case students need it. Should it go somewhere else? Should I introduce it in a different way?

[siwelwerd]

This seems like a good place for it, but as is there is no exploration of why we might expect it to be true--it is just a formula handed to students.

I think an exploration could walk them through it in two steps. First, show $\log _b d = \frac{1}{\log _d b}$ (e.g., by rewriting $y=\log_b d$, solving for $b$, then $\log _a b=\frac{1}{y}$). Then, walk them through $\log _b a = \log _b \left(d^{\log _d a}\right) = \left(\log _d a \right) \left(\log _b d\right) = \frac{\log _d a}{\log _d b}$.

Or maybe there's a better quick derivation, that's just the one I scratched out off the top of my head.

[tdegeorge]

Ok, added in another activity for change of base....let me know if that works!