Question

Given log₁₀ a = m, log₁₀ b = n, log₁₀ c = p, express k in terms of a, b and c if k = 10^{2m + 3n – 5p}.

Answer 1

Given, log₁₀ a = m ⇒ a = 10^m

log₁₀ b = n ⇒ b = 10ⁿ

log₁₀ c = p ⇒ c = 10^p

Substitute these values in the expression for k:

k = 10^{2m + 3n – 5p}

Separate the powers:

k = 10^2m × 10³ⁿ × 10^−5p

Now substitute:

10^2m = a²

10³ⁿ = b³

10^−5p = `1/c^5`

So k = `a^2 xx b^3 xx 1/c^5`

k = `(a^2b^3)/c^5`