M5.2.3 For the adult
Laws of logarithms
Logarithms are powers, so they should follow the laws of powers. What do they let us do with a product, a quotient and a power?
What this chapter teaches
Logarithms follow the laws of powers. The log of a product is the sum of the logs. The log of a quotient is the difference. The log of a power is the power times the log. A sum inside a log cannot be split. The change of base formula, log x ÷ log a, lets a calculator find a log to any base.
Three questions to ask
There is no one right wording. Listen for the idea.
- How can you write log 6 as a sum of two logs, and why is that true?
- When you try both on a calculator, why is log (10 + 10) not the same as log 10 + log 10?
- How would you find log₅ 40 if your calculator only has a log key for base 10?
After the chapter, the learner can
- Use the laws for the log of a product, quotient and power
- Write 2 log 3 + log 4 as one logarithm
What they copy into their notebook
log xy = log x + log y. log (x/y) = log x − log y. log (xⁿ) = n log x. Same base. No law for log (x + y). Change of base: the log of x to base a is log x ÷ log a.