3.2 Indices

LCHL - Indices

LCHL - Logs

Representing numbers as squares, cubes, square roots, and reciprocals

I should be able to:

Foundation Level

– solve contextual problems involving numbers represented in the following ways:√a, a1/2 , a2, a3 , 1/a

Ordinary Level

– solve problems using the rules for indices (where a, b ∈ R; p, q ∈ Q; ap, aq∈ Q; a, b ≠ 0):

• a^pa^q = a^p+q

• a^p/a^q = a^p-q

• a⁰ = 1

• (a^p)^q = a^pq

• a^1/q = ^q√a (q ∈ Z, q ≠ 0, a>0)

• a^p/q = ^q√a^p = (^q√a)^p (p,q ∈ Z, q ≠ 0, a>0)

• a^-p = 1/a^p

• (ab)^p = a^pb^p

• (a/b)^p = a^p/b^p

Higher Level

– solve problems using the rules of logarithms

• log_a x y = log_a x + log_a y

• log_a (x/ y) = log_a x - log_a y

• log_a x ^q = qlog_a x

• log_a a = 1, log_a 1 = 0

• log_a x = log_b x / log_b a