Grade 12 · Theory
Logarithms
Functions and inverses · about 3 min
Visual overview: Logarithms1 MIN READ
2 study sections · pause after each one and recall the key ideaThe logarithm is the inverse of the exponential, which is why it solves for exponents.
Key points- y = bˣ has inverse y = log_b x.
- log(ab) = log a + log b; log(a/b) = log a − log b; log(aⁿ) = n·log a.
- Change of base: log_b a = log a / log b.
- log x is defined only for x > 0.
- Logarithm — the exponent to which a base must be raised.
EXAM TIP
use logs the moment the unknown sits in an exponent and the bases refuse to match.