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What is the domain of the function log(log(sinx))?
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All possible values that x can take i.e. x $\in$$\mathbb{R}$.
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the graph of log x is given below :-

So, log x is defined for x > 0

So, according to question ,

log(logsinx) will be defined when log(sinx) > 0

So, log(sinx) >0

So, sinx > e0

sinx > 1

Since , we know that -1<=sinx <=1

but we got sinx >1

So, we can say no 'x' is existed here.

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