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Leg f(x)=log((log)(1//3)((log)(1/3)((log...

Leg `f(x)=log((log)_(1//3)((log)_(1/3)((log)_7(sinx+a)))` be defined for every real value of `x ,` then the possible value of `a` is 3 (b) 4 (c) 5 (d) 6

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`log_(1//3)log_6(sinx+a)gt0`
`or 0ltlog_7(sinx=a)lt1`
`or 1lt(sinx+a)lt7,AA x in R`
`or 1-sixltalt7-sinx`
It is found that a should by less thanthe minimum value of (7 - sinx) and a must be greater the the maximum value of (1 - sinx). Thus,
`rArr 2ltalt6`
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