How do you solve for y in terms of x in this logarithmic equation?

Question

log x + 2 log y = 3 log 2

Answers are given as y = 2 x sqrt(2/x) / -2 x sqrt(2/x) (rejected) or y = sqrt(8/x) / y=-sqrt(8/x) (rejeted)

I got 10^[log10(8/x)]/2, how do I solve for y in a manner that will get me one of the answers above?

Answer 1

log(x) + 2 log(y) = 3 log2

2 log(y) = 3 log2 - log(x)

log(y²) = log(2³) - log(x)

log(y²) = log(2³/x) = log(8/x)

Take 10⁽⁾ of both sides.

y² = 8/x

y = √(8/x) = 2√(2/x)