If 5^{x + 1} = 25^{x - 2}; find the value of : 3^{x - 3} × 2^{3 - x}.

Question

KnowledgeBoat · Accepted Answer

Given, ⇒ 5^{x + 1} = 25^{x - 2} ⇒ 5^{x + 1} = (5²)^{x - 2} ⇒ 5^{x + 1} = 5^{2(x - 2)} ⇒ x + 1 = 2(x - 2) ⇒ x + 1 = 2x - 4 ⇒ 2x - x = 1 + 4 ⇒ x = 5. Substituting value of x in 3^{x - 3} × 2^{3 - x}, we get : ⇒ 3^{x - 3} × 2^{3 - x} = 3^{5 - 3} × 2^{3 - 5} = 3² × 2^(-2) = . Hence, 3^{x - 3} × 2^{3 - x} = .

Mathematics

If 5^{x + 1} = 25^{x - 2}; find the value of :
3^{x - 3} × 2^{3 - x}.

Indices

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