Question

If log₁₀ x = m, log₁₀ y = n, write 10^{3m + 1} in terms of x.

Answer 1

Given, log₁₀ x = m

⇒ x = 10^m

We are to express 10^{3m + 1} in terms of x.

Split the exponent:

10^{3m + 1} = 10^3m × 10¹

Now express 10^3m in terms of x:

x³ = (10^m)³ = 10^3m

So 10^{3m + 1} = x³ × 10

10^{3m + 1} = 10x³