Logarithms
A logarithm is an exponent: log_b(x) = y means b^y = x.
The rules
- Rewrite logs as exponents to solve.
- log(ab) = log a + log b. log(a/b) = log a − log b. log(aⁿ) = n log a.
- log_b(b) = 1 and log_b(1) = 0.
- Logs undo exponentials.
Watch out: Treating log(a + b) as log a + log b.
Worked example
What is log₂ 32?
- 2^y = 32.
- 2⁵ = 32, so y = 5.
Answer: 5
Try it yourself
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