urp:power

Combining powers

nᵃnᵇ = nᵃ⁺ᵇ nᵃ/nᵇ = nᵃ⁻ᵇ (nᵃ)ᵇ = nᵃᵇ n⁻ᵃ = 1/nᵃ

(Note: The square root sign, √, refers only to the *positive* root. Use ± to include both roots.)

Log is the inverse of a power

x = bᵉ, e = logᵦ(x) (b = base, 10 by default) eg. 2³ = 8, log₂(8) = 3 log(1) = 0 (for any base), log(x) is undefined for x =< 0 logₐ(x) = logᵣ(x) / logᵣ(a) = log(x) / log(a) for r=10 = ln(x) / ln(a) for r=e (e = Euler's number, 2.718..) natural log: ln(x) = logₑ(x) ln(e) = 1, log(10) = 1 eᵏ = c, and k = ln(c) => e^ln(c) = c

a^logₐ(x) = x (power and log are inverses, cancel each other out) logₐ(aᵏ) = k (same reason) product rule: log(ab) = log(a) + log(b) quotient rule: log(a/b) = log(a) - log(b) power rule: log(aᵇ) = b*log(a)

urp/power.txt · Last modified: 2021-11-16 by nerf_herder