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The number of solutions of "log"("sin"x)...

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

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
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.
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OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Section I - Solved Mcqs
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  13. IF x=198! then value of the expression 1/(log2x)+1/(log3x)+...+1/(log1...

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  16. If log(0.04) (x-1)>=log(0.2) (x-1) then x belongs to the interval

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  17. If "log"(a) x xx "log"(5)a = "log"(x) 5, a ne 1, a gt 0, " then "x =

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  18. If log(0.5) sin x=1-log(0.5) cos x, then number of values of x in [-2p...

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  19. If x1,x2,x3,... are positive numbers in G.P then logxn, logx(n+1), log...

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