3 votes 3 votes The domain of the function $\log (\log \sin(x))$ is: $0<x<$$\pi$ $2n$$\pi$$<$$x$$<$$(2n+1)$$\pi$, for $n$ in $N$ Empty set None of the above Calculus isro2018 calculus functions + – Arjun asked Apr 22, 2018 recategorized Dec 8, 2022 by Lakshman Bhaiya Arjun 5.4k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 12 votes 12 votes log( log sin(x) ) -1 <= sinx<= +1 log a is defined for positive values of a, log sin(x) is defined for sin(x)= (0,1] Possible values for log sin(x) = ($-\infty$ , 0] Domain of log( log sin(x) )=Not defined Therefore, Answer (c) Empty Set VS answered Apr 23, 2018 edited Apr 26, 2018 by VS VS comment Share Follow See all 2 Comments See all 2 2 Comments reply maahisingh commented Apr 24, 2018 reply Follow Share there is a difference between range and domain of a function, Question is asking domain not range. 0 votes 0 votes ankitgupta.1729 commented Apr 24, 2018 reply Follow Share * log sin(x) is defined for sin(x)= (0,1] 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes Option C is correct. We can satisfy inner log using $x=\pi / 2$, but can't satisfy outer log at the same time. Thus, empty set. Akhilesh Singla answered Apr 22, 2018 Akhilesh Singla comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes $\log sin(x)>0 => sin (x)>e^0.$ Now this is impossible because the value of sin cannot be greater than 1. Therefore, empty set is the answer. Asim Siddiqui 4 answered Jun 8, 2020 Asim Siddiqui 4 comment Share Follow See all 0 reply Please log in or register to add a comment.