To solve this equation, we need to simplify both sides and then isolate the variable x.

Starting with the left side:
2/3 * x - 1/3

To combine the fractions, we need a common denominator, which is 3:
(2x - 1) / 3

Now let's simplify the right side:
(3/4)^5 / (3/4)^3

To simplify the exponents, we subtract them:
(3/4)^(5-3) = (3/4)^2 = 9/16

So the equation becomes:
(2x - 1) / 3 = 9/16

To isolate x, we can cross multiply:
16(2x - 1) = 3(9)

Simplifying both sides:
32x - 16 = 27

Adding 16 to both sides:
32x = 43

Dividing both sides by 32:
x = 43/32

Therefore, the solution to the equation is x = 43/32.