The equation \( \sqrt{1+\log _{x} \sqrt{27}} \log _{3} x+1=0 \) has (1) no integral solution (2)...

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The equation \( \sqrt{1+\log _{x} \sqrt{27}} \log _{3} x+1=0 \) has
(1) no integral solution
(2) one irrational solution
(3) two real solutions
(4) no prime solution
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