8分之27的x-1次方乘以3分之2的2x-3次方等于9分之4,求x的值

(27/8)^(x-1)乘以(2/3)^(2x-3)=9/4
(3/2)^3(x-1)乘以(2/3)^(2x-3)=(3/2)^2
(3/2)^(3x-3)乘以(2/3)^(2x-3)=(3/2)^2
由(3/2)^(2x-3)乘以 (3/2)^x 乘以(2/3)^(2x-3)=(3/2)^2
得 (3/2乘以2/3)^(2x-3)乘以 (3/2)^x =(3/2)^2
1^(2x-3)乘以 (3/2)^x =(3/2)^2 又 由 1^(2x-3)=1
得 (3/2)^x =(3/2)^2
所以x=2