To solve this logarithmic equation, we first need to simplify the terms using the properties of logarithms.

Given equation: 2*log8$2x$ + log8$x-1$^2 = 4/3

Using the properties of logarithms, we can rewrite log8$2x$ as log8$2$ + log8$x$. Similarly, log8$x-1$^2 can be rewritten as 2*log8$x-1$.

Therefore, the equation becomes: 2$log8(2)+log8(x)$ + 2log8$x-1$ = 4/3.

Now, we will use the property of logarithms which states that a*logb$c$ = logb$c$^a to simplify the equation further.

The equation becomes: log8$2^2$ + 2*log8$x$ + log8$(x-1{)}^2$ = 4/3
Simplify this further:
log8$4$ + log8$x^2$ + log8$(x-1{)}^2$ = 4/3

Now, we can combine the logarithmic terms using the property of adding logarithms of the same base.

log8$(4)<em>(x^2)</em>((x-1{)}^2)$ = 4/3

Now we can express the equation using the formula logb$mn$ = logb$m$ + logb$n$.

log8$4$ + log8$x^2$ + log8$(x-1{)}^2$ = 4/3
log8$4<em>(x^2)</em>((x-1{)}^2)$ = 4/3
log8$4x^2(x-1{)}^2$ = 4/3

Now rewrite the equation in exponential form:
8^$4/3$ = 4x^2$x-1$^2

Simplify the left side:
$2^3$^4/3 = 4x^2$x-1$^2
2^4 = 4x^2$x-1$^2
16 = 4x^2$x-1$^2

Now, we can solve for x by dividing both sides by 4 and then taking the square root of both sides:
16/4 = x^2$x-1$^2
4 = x^2$x-1$^2
2 = x$x-1$

Now, we can solve for x by setting x$x-1$ = 2 to zero:
x^2 - x - 2 = 0
$x-2$$x+1$ = 0
x = 2 or x = -1

Therefore, the solutions to the given logarithmic equation are x = 2 and x = -1.