Question

If log ₁₀ x = a, log ₁₀ y = b and log ₁₀ z = 2a - 3b, express z in terms of x and y.

Answer 1

log ₁₀ x = a
⇒ x = 10 ^a
log ₁₀ y = b
⇒ y = 10 ^b
log ₁₀ z = 2a - 3b
⇒ z = 10^2a-3b 
∴ z = 10^2a-3b 
= (10 ^a)² . (10 ^b)^-3
= (x)² (y)^-3
= `x^2/y^3`.