Why does my child think log 2 + log 3 = log 5?
Your child adds the numbers inside logs, such as log 2 + log 3 as log 5 instead of log 6.
Why children do it
It looks like ordinary adding, so the numbers get added. But a log is a power, and adding powers multiplies: log 2 + log 3 = log 6. Trying it with numbers whose logs are known, like log₂ 4 + log₂ 8 = 2 + 3 = 5, shows it, since 2⁵ = 32 = 4 × 8.
How to help at home
Ask them to try it with powers: log₂ 4 + log₂ 8 is 2 + 3 = 5, and 2⁵ is 32, which is 4 × 8.
The right way
Write log₂ 4 + log₂ 8 as one log, log₂ k. What is k?
- 4 × 8 = 32Adding logs multiplies the numbers.
- 32So k = 32.
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