LIST OF IMPORTANT MATH FORMULAS AND RESULTS

 

LIST OF IMPORTANT MATH FORMULAS AND RESULTS

Algebra:

Laws of Indices:

(i) aᵐ ∙ aⁿ = aᵐ + ⁿ

(ii) aᵐ/aⁿ = aᵐ - ⁿ

(iii) (aᵐ)ⁿ = aᵐⁿ

(iv) a = 1 (a ≠ 0).

(v) a-ⁿ = 1/aⁿ

(vi) ⁿ√aᵐ = aᵐ/ⁿ

(vii) (ab)ᵐ = aᵐ ∙ bⁿ.

(viii) (a/b)ᵐ = aᵐ/bⁿ

(ix) If aᵐ = bᵐ (m ≠ 0), then a = b.

(x) If aᵐ = aⁿ then m = n.

 Logarithm:

(i) If a^x = M then log_a M = x and conversely.

(ii) log_a 1 = 0.

(iii) log_a a = 1.

(iv) a ^log_am = M.

(v) log_a MN = log_a M + log_a N.

(vi) log_a (M/N) = log_a M - log_a N.

(vii) log_a Mⁿ = n log_a M.

(viii) log_a M = log_b M x log_a b.