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7^(x+3) + 7^(x+4) = 2744     factor

7^(x+3) ( 1 + 7) = 2744

7^(x + 3) (8)  = 2744   divide both sides by 8

7^(x + 3)  = 343

7^(x + 3)  =  7^3      →  x  =  0

what cphill said