Question 1205441
<pre>

It has occurred to me that 

{{{X^(2n)^""}}} and {{{("" +- X^"")^(2n)}}} mean the same for any positive integer n.

So for any positive even integer 2n, we can always replace {{{X^(2n)^""}}} with {{{("" +- X^"")^(2n)}}}. 
So this problem should make use of this substitution at the very beginning.

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{{{log(5,((3x-2)^4))}}}{{{""=""}}}{{{8}}}

{{{log(5,(("" +- (3x-2)^"")^4))}}}{{{""=""}}}{{{8}}}

{{{4*log(5,("" +- (3x-2)^""))}}}{{{""=""}}}{{{8}}}

{{{log(5,("" +- (3x-2)^""))}}}{{{""=""}}}{{{2}}}

{{{"" +- (3x-2)}}}{{{""=""}}}{{{5^2}}}

{{{3x-2}}}{{{""=""}}}{{{"" +- 25}}}

3x-2 = 25    3x-2 = -25
  3x = 27      3x = -23
   x = 9        x = -23/3

Edwin</pre>