Question

The number of solutions of `"log"_("sin"x)(2^(" tan"x)) gt 0` in the interval `(0, pi//2)` is

Answer 1

Correct Answer - A
We have,
`"log"_("sin"x)2^(" tan"x) gt 0 rArr 2^("tan"x) lt ("sin" x)^(0) rArr 2^("tan"x) lt 1`
But, `2^("tan"x) cancel(lt)1 " for any " x in (0, pi//2)`
Hence, the given inequation has no solution.