Given (1/logy 4) = (log1/4 1/8x), express y as a polynomial function of x.

It's easier if the equation is posted in an unambiguous form. Parentheses wouldn't hurt.

Bases of logarithms can be posted using the "subscript" tags, for example, log_e10 can be posted as
"log < s u b > e < / s u b > 10"
but without the intervening spaces and double quotes.

(log1/4 1/8x) could be interpreted as
log(1/4)*(x/8), or
log(1/4)*(1/(8x)), or
log((1/4)*(x/8)), or
log((1/4)*(1/(8x))), or
log((1/((4 1/8)x))), [ i.e. fraction] or
log((1/((4 1/(8x)))

Again, extra parentheses don't hurt.