Exponents and logarithms

Remedial refresher on powers and logs: what log₂ x asks, why logs of probabilities are negative, the log rules, and switching between log₂, log₁₀ and ln.

Prerequisites: multiplication, fractions and basic algebra only.

6 lessons · 2 written so far

  1. 1Powers of two, both waysStartExponents including zero and negatives, and log₂ as "how many doublings"; why −log₂ p needs its minus sign.
  2. 2The log rulesStartProduct, quotient and power rules, derived from exponents; why surprises add.
  3. 3Logs of anythingNot written yetLogs of numbers that aren't neat powers (log₂ 27 ≈ 4.75), estimating between powers, and the shape of the log curve.
  4. 4Changing baseNot written yetlog₁₀, ln and the change-of-base formula; bits versus nats.
  5. 5e and the natural logNot written yetWhere e comes from (compounding), exponential growth and decay, and why ML code uses ln.
  6. 6CheckpointNot written yetMixed practice in information-theory settings: surprise, entropy and loss.