Question

If log₁₀ x = m, log₁₀ y = n, write 10^{2n – 3} in terms of y.

Answer 1

Given, log₁₀ y = n

⇒ y = 10ⁿ

We are to express 10^{2n – 3} in terms of y.

Split the exponent:

10^{2n – 3} = 10²ⁿ × 10⁻³

Now express 10²ⁿ in terms of y:

y² = (10ⁿ)² = 10²ⁿ

So 10^{2n – 3} = y² × 10⁻³

`10^(2n - 3) = y^2/1000`