Question

Let $f\left(x\right)=\log ({\log }_{1/3}\left({\log }_7\right(\sin x+a\left)\right))$ be defined for every value of $x$, then the possible value of $a$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (A), (B), (C)

$5$

${\log }_{1/3}\left({\log }_7\right(\sin x+a\left)\right)>0$
$\Rightarrow 0<{\log }_7(\sin x+a)<1$
$\Rightarrow 1<\sin x+a<7,\forall x\in R$
$\Rightarrow 1-\sin x<a<7-\sin x$
This means $a$ should lie in between the maximum value of $(1-\sin x)$ and the minimum value of $(7-\sin x)$
$\therefore 2<a<6$