First, students will learn what the change of base formula is, and why it's true. After that, students will learn how to evaluate logarithms on a calculator, using the change of base formula. Most scientific calculators will have a button for \(\log_{10}.\) Students can evaluate an expression such as \(\log_2 10,\) by plugging in \(\log_{10} 10 / \log_{10} 2,\) which is equivalent, according to the change of base formula. Students will also learn how to bound \(\log\) expressions between integers. For example, \(3 < \log_2 10 < 4,\) because \(2^3 < 10 < 2^4.\) Bounding expressions in this way is good for checking that your calculator answer is correct. If I input \(\log_2 10\) into my calculator, I get \(3.32\ldots\) which is likely correct, since I know \(\log_2 10\) is somewhere between 3 and 4.

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Conclude by giving your students these challenges:

- The Games' Medals by NRICH
- Route Product by NRICH
- Make 100 by NRICH
- 2001 AMC 8, Problem 12
- 2007 AMC 8, Problem 1