3^(x+2)=54+3^(x+1)

We can rewrite this as

(3^x)(3²)= 54 + (3^x)(3)         divide through by 3

(3^x)(3) = 18 + 3^x               subtract 3^x from both sides

(3^x)(3) - 3^x  = 18               factor the left side

(3^x)(3 - 1) = 18               simplify the left side

(3^x)(2) = 18                    divide both sides by 2

3^x = 9      ... so it appears that x = 2