M5.2.2 For the adult
Logarithms
We can solve 2ˣ = 32 by counting powers of 2. How do we write, and find, the answer to 2ˣ = 20?
What this chapter teaches
A logarithm is a power. The statement log₂ 32 = 5 says that 2 to the power 5 is 32. The number inside a log must be above 0, and the base must be above 0 and not 1. The graph of y = log₂ x is the mirror image of y = 2ˣ in the line y = x.
Three questions to ask
There is no one right wording. Listen for the idea.
- How would you write 3⁴ = 81 as a logarithm, and say it aloud?
- Why can nobody work out log₂ of −4?
- What is log₇ 1, and what is log₇ 7? How do you know without a calculator?
After the chapter, the learner can
- Change 2⁵ = 32 into log₂ 32 = 5
- Work out log₃ 81 without a calculator
What they copy into their notebook
The log of b to the base a is x means aˣ = b (a > 0, a ≠ 1, b > 0). The log of 1 is 0. The log of the base is 1. The log undoes aˣ.