#### Answer

$x=3$

#### Work Step by Step

RECALL:
For any non-negative real number $a$,
$\left(a^{\frac{1}{4}}\right)^4=a$
Raise both sides of the equation to the fourth power then sue the rule above to simplify.
$\left((x-2)^{\frac{1}{4}}\right)^4=\left((3x-8)^{\frac{1}{4}}\right)^4
\\x-2=3x-8$
Subtract $x$ and add $8$ on both sides of the equation to obtain:
$-2+8=3x-x
6=2x$
Divide 2 on both sides to obtain:
$3=x$