Given log₁₀ x = a, log₁₀ y = b,

(i) Write down 10^{a + 1} in terms of x.

(ii) Write down 10^2b in terms of y.

(iii) If log₁₀ P = 2a − b, express P in terms of x and y.

Given,

⇒ log₁₀ x = a and log₁₀ y = b

⇒ x = 10^a and y = 10^b

(i) Given,

⇒ 10^{a + 1}

⇒ 10^a × 10¹

⇒ x × 10

⇒ 10x.

Hence, 10^{a + 1} = 10x.

(ii) Given,

⇒ 10^2b

⇒ (10^b)²

⇒ y².

Hence, 10^2b = y².

(iii) Given,

⇒ log₁₀ P = 2a − b

⇒ P = 10^{(2a − b)}

⇒ P = 10^2a × 10^−b

⇒ P = (10^a)² × (10^b)^-1

⇒ P = (x)² × (y)^-1

⇒ P = $\dfrac{x^2}{y}$.

Hence, P = $\dfrac{x^2}{y}$.