If 3^{x-1}+3^{3-x}=6 then what is 2^{x-1}+2^{3-x} equal to?

Explanation

Let 3^{x-1} = y. The equation rewrites as y + \frac{3^2}{y} = 6 \implies y^2 - 6y + 9 = 0. Solving gives y=3. Thus, 3^{x-1} = 3^1 \implies x=2. Substituting x=2 into the second expression: 2^{2-1} + 2^{3-2} = 2^1 + 2^1 = 4.

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