Students will learn how to evaluate logarithmic expressions using the one-to-one property. That is, if \(x^a = x^b,\) then \(a = b.\) Students should see problems where the answer is an integer or rational.

Conclude by giving your students these challenges:

- Bipin's Choice by NRICH
- Fencing by NRICH
- 2017 AMC 8, Problem 24

Express abs in terms of max. The answer is

$$\lvert x \rvert = \max(x, -x)$$

Express \(\max\) in terms of \(\text{abs}.\) Then use your answer to express \(\max(x, 0)\) and \(\min(x, 0)\) in terms of \(\text{abs}.\) The answer is

$$\begin{align}
& \max(x, y) = \dfrac{x + y + \lvert x - y \rvert}{2} \\[1em]
& \max(x, 0) = \dfrac{x + \lvert x \rvert}{2} \\[1em]
& \min(x, 0) = \dfrac{x - \lvert x \rvert}{2}
\end{align}$$