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(3/10)(4/9)(3/2)^x = (6/5)(8/27)(3/2)^x - 1/2
(3/2)^x = y
(3/10)(4/9)y = (6/5)(8/27)y - 1/2
(2/15)y = (16/45)y - 1/2
(10/45)y = 1/2
(2/9)y = 1/2
y = 9/4
(3/2)^x = 9/4
(3/2)^x = (3/2)²
x = 2