Evaluating logarithms

Students will be introduced to logarithms, and learn to evaluate logarithms when...

• the argument is some power of the base, such as \(\log_2 8\), \(\log_3 9\), or \(\log_7 1\).
• the base is some power of the argument, such as \(\log_8 2\), \(\log_9 3\), or \(\log_1 7\).
• the argument is the reciprocal of some power of the base, such as \(\log_2 \dfrac{1}{8}\) or \(\log_3 \dfrac{1}{9}\).
• the argument or the base is a square root, such as \(\log_\sqrt{3} 9\) or \(\log_6 \sqrt{6}\).

Students will also learn why the logarithm is undefined for many choices of its base and argument. To teach this idea, I recommend watching this, then this. Conclude by giving your students this challenge.