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We have to solve the equation 9^(x-1)=27^(x+1) for x.

9^(x-1)=27^(x+1)

=> 9^x/ 9 = 27^x * 27

=> 9^x / 27^x = 27*9

=> 3^2x / 3^3x = 3^5

=> 3^(2x - 3x) = 3^5

As the base 3 is the same we can equate the exponential

=> -x = 5

=> x = -5

The required value of x is -5.

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