If log₂x = a and log₅y = a, write 100^{2a - 1} in terms of x and y.

Question

KnowledgeBoat · Accepted Answer

Given, log₂x = a and log₅y = a ⇒ x = 2^a and y = 5^a 100^{2a - 1} = 100^2a.100^-1 = (100^a)².100^-1 = [(2².5²)^a]².100^-1 = [(2^2a).(5^2a)]².100^-1 = [(2^a)².(5^a)²]².(100)^-1 = [x².y²]².100^-1 = . Hence, 100^{2a - 1} = .

Mathematics

If log₂x = a and log₅y = a, write 100^{2a - 1} in terms of x and y.

Logarithms

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