Given log^10 x = 2a and log^10 y = b/2, (i) write 10^a in terms of x. (ii) write 10^2b + 1 in terms of y. (iii) if log^10 P = 3a - 2b, express P in terms of x and y.

Question

KnowledgeBoat · Accepted Answer

(i) Given, log₁₀x = 2a ⇒ x = 10^2a ⇒ x = (10^a)² ⇒ 10^a = . Hence, 10^a = . (ii) Given, log₁₀y = Squaring both sides we get, ⇒ y² = 10^b Simplifying 10^{2b + 1} we get, 10^{2b + 1} = 10^2b.10 = (10^b)².10 = (y²)².10 = 10y⁴. Hence, 10^{2b + 1} = 10y⁴. (iii) Given, log₁₀P = 3a - 2b ⇒ P = 10^{3a - 2b} ⇒ P = 10^3a.10^-2b = (10^a)³.(10^b)^-2 Hence, P = .

Mathematics

Given log^10 x = 2a and log^10 y = b/2, (i) write 10^a in terms of x. (ii) write 10^2b + 1 in terms of y. (iii) if log^10 P = 3a - 2b, express P in terms of x and y.

Logarithms

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Mathematics

Given log^10 x = 2a and log^10 y = b/2, (i) write 10^a in terms of x. (ii) write 10^2b + 1 in terms of y. (iii) if log^10 P = 3a - 2b, express P in terms of x and y.

Logarithms

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