The domain of the function $$f(x)=log2$$⁡$$log2$$⁡$$log2$$⁡…$$log2$$⁡x⏟n times is

Question

The domain of the function $$f(x)=log2$$⁡$$log2$$⁡$$log2$$⁡…$$log2$$⁡x⏟n times  is

Infinity Learn · Accepted Answer

f (x) is defined $$if(1)$$ x>$$0$$  (2) $$log2$$⁡x>$$0$$⇒x>$$20=1$$  (3) $$log2$$⁡$$log2$$⁡x>$$0$$⇒$$log2$$⁡x>$$20=1$$⇒x>$$21=2$$  (4) $$log2$$⁡$$log2$$⁡$$log2$$⁡x>$$0$$⇒$$log2$$⁡$$log2$$⁡x>$$20=1$$                                    ⇒$$log2$$⁡x>$$21=2$$                                   ⇒x>$$22$$  (5) $$log2$$⁡$$log2$$⁡$$log2$$⁡$$log2$$⁡x>$$0$$⇒$$log2$$⁡$$log2$$⁡$$log2$$⁡x>$$20=1$$                                            ⇒$$log2$$⁡$$log2$$⁡x>$$21$$                                           ⇒$$log2$$⁡x>$$22$$⇒x>$$222Continuing$$ like this, we get x>$$222(n$$−$$1)times$$∴ Domain of $$f=222$$.(n$$−$$1) iimes ,∞

The domain of the function $f (x) = \underset{n times}{\underset{⏟}{\log_{2} \log_{2} \log_{2} \dots \log_{2} x}} is$

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The domain of the function f(x)=log2⁡log2⁡log2⁡…log2⁡x⏟n times is

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The domain of the function $f (x) = \underset{n times}{\underset{⏟}{\log_{2} \log_{2} \log_{2} \dots \log_{2} x}} is$