A logarithm answers the question: what power? log₃ 243 = 5 because 3⁵ = 243. In general, logₐ b = c means aᶜ = b.
The log laws match the index laws. log a + log b = log(ab), log a − log b = log(a/b) and log aⁿ = n log a, all with the same base. So log₂ 192 − log₂ 12 = log₂ 16 = 4. Also logₐ a = 1 and logₐ 1 = 0.
Worked example
Find the value of log₅ 20 + log₅ (1/4).
- Add the logs: log₅ (20 × 1/4) = log₅ 5.
- log₅ 5 = 1.
Answer:1
Key words
- logarithm
- the power a base must be raised to
- base
- the number being raised to a power
- log laws
- rules for adding, subtracting and powers of logs
Practise this
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Common Core-referenced: HSF-LE.A.4