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Mathematics

If 3^{x + 1} = 9^{x - 2}, find the value of 2^{1 + x}.

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Answer

Given,

⇒ 3^{x + 1} = 9^{x - 2}

⇒ 3^{x + 1} = (3²)^{x - 2}

⇒ 3^{x + 1} = 3^{2(x - 2)}

⇒ 3^{x + 1} = 3^{2x - 4}

⇒ x + 1 = 2x - 4

⇒ 2x - x = 1 + 4

⇒ x = 5.

Substituting value of x in 2^{1 + x} we get,

⇒ 2^{1 + x} = 2^{1 + 5} = 2⁶ = 64.

Hence, 2^{1 + x} = 64.

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