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Question

# Find the domain of the function :f(x)=√log(logx)−log(4−logx)−log3

A
(103,104)
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B
[103,104]
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C
[103,104)
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D
(103,104]
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Solution

## The correct option is C [103,104) formulaused logm+logn=log(mn) logm−logn=log(mn) f(x)=√log(logx)−log(4−logx)−log3 log(logx)−log(4−logx)−log3≥0 ⇒log(logx)−[log(4−logx)+log3]≥0 ⇒log(logx)−[log(12−3logx)]≥0 ⇒log[logx12−3logx]≥0 ⇒logx12−3logx≥100 ⇒logx12−3logx≥1 case1 if12−3logx>0 logx≥12−3logx ⇒4logx≥12 ⇒logx≥3 x≥103 cas2 3logx<12 ⇒logx<x x<104 Hencedomain:[103,104)

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