Question

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

Answer 1

log₁₀ a = b
⇒ 10^b = a

⇒ ( 10^b )³ = a³    ...[ Cubing both sides ]

⇒ `10^(3b)/10^2 = a^3/10^2`  ...[dividing both sides by 10²]

⇒ 10^{3b - 2} = `a^3/100`