Question

Given log₁₀ a = m and log₁₀ b = n, express a³/b² in terms of m and n.

Answer 1

Given:

log₁₀ a = m

(10)^m = a

log₁₀ b = n

(10)ⁿ = b .......(1 mark)

So,

a³/b² = (10^m)³ / (10ⁿ)²

= 10^3m / 10²ⁿ

= 10^{3m – 2n} ........(1 mark)