Math basics › Exponents and logs
Logarithms
What a log is
log₇(x) asks: what power of b gives x? log₂(8) = 3 because 2³ = 8. It is the inverse of an exponential.
The rules
log(ab) = log a + log b. log(a/b) = log a − log b. log(aⁿ) = n log a. Logs turn multiplying into adding.
Which base
log usually means base 10. ln means base e. Change base with log₇(x) = ln x / ln b.
The domain
You can only take a log of a positive number. Solutions that make the inside zero or negative must be thrown out.