Solve for x: 2^x+2^(x+1)+2^(x-1)=56

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We have 2^x+2^(x+1)+2^(x-1)=56

Now 2^x+2^(x+1)+2^(x-1)=56

=> 2^x + 2^x*2 + 2^x / 2 = 56

=> 2^x (1 + 2 + 1/2) = 56

=> 2^x * 7/2 = 56

=> 2^x = 56*2 / 7

=> 2^x = 16

=> 2^x = 2^4

As the base is the same for 2^x and 2^4, we can equate the exponent.

Therefore x = 4.

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