VG2
tall-og-algebra
Quiz
What are logarithms?
The logarithm is the inverse of exponentiation. It answers: what exponent do we need to produce a given number?
Definition
log_a(x) = y ⟺ aʸ = x
Common logarithms
| Notation | Base | Name |
|---|---|---|
| log(x) | 10 | Common logarithm |
| ln(x) | e | Natural logarithm |
| log₂(x) | 2 | Binary logarithm |
Examples
log₁₀(1000) = 3 · log₂(8) = 3 · ln(e) = 1
Logarithm rules
log(a·b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(aⁿ) = n·log(a)
log(a/b) = log(a) - log(b)
log(aⁿ) = n·log(a)
Rule of 72: Years to double ≈ 72 / interest rate. At 6%: 72/6 = 12 years.
Seeing there is nothing that is so troublesome to mathematical practice as the multiplications, divisions and extractions of roots of great numbers, I began to consider a method that would remove these obstacles.
— John Napier (1550–1617), inventor of logarithms
🧠 Test yourself
Question 1 of 3
What is log₂(16)?