JEE Advance - Mathematics (1989 - No. 10)

The equation $${x^{3/4{{\left( {{{\log }_2}\,\,x} \right)}^2} + {{\log }_2}\,\,x - 5/4}} = \sqrt 2 $$ has
at least one real solution
exactly three solutions
exactly one irrational solution
complex roots.

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