Solving equation (4 / 9) ^ x multiplied by (27 / 8) ^ X-1 = 2 / 3 Just talk about the train of thought

Solving equation (4 / 9) ^ x multiplied by (27 / 8) ^ X-1 = 2 / 3 Just talk about the train of thought

[(2/3)^2]^x*[(3/2)^3]^(x-1)=2/3 (2/3)^2x*(3/2)^(3x-3)=2/3 (2/3)^2x*(3/2)^2x*(3/2)^(x-3)=2/3 [(2/3)*(3/2)]^2x*(3/2)^(x-3)=2/3 1^2x*(3/2)^(x-3)=(3/2)^(-1) (3/2)^(x-3)=(3/2)^(-1) x-3=-1 x=2