I find your lack of parentheses ... disturbing
I shall solve
log_3(√x) + 1/2 = 3/log_3(x)
Now, assuming base 3 for the logs,
1/2 logx + 1/2 = 3/logx
log^2(x) + logx - 6 = 0
(logx+3)(logx-2) = 0
logx = -3 or 2
x = 1/27 or 9
you can easily check that both solutions work
Solve for x:
Log base 3 square root of x +1/2 = 3log base x 3
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