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What is the domain of the function \(f(x)=\log_2(\log_3(\log_4x))\)?

 Feb 5, 2021
 #1
avatar+118470 
+1

We cannot take the log  of  0  or a negative

 

So....the domain is    (0,  inf )

 

cool cool cool

 Feb 5, 2021
 #2
avatar+128 
+1

shouldn't it be (4, inf)? i am not sure, though...

macar0ni  Feb 5, 2021
 #3
avatar+118470 
+1

Yeah..I see what you mean..let  me  think  about this

 

If x  = 4

 

Log 3 ( 1)   = 0

 

So  if x  >  4

log  4  ( x)   >   1

 

So  log3  ( x > 1)   will  be  >   0

 

So  log 2  (something >  0)   will exist

 

So...I think you are correct   macar0ni    ....   (4, inf)   !!!

 

THX for  pointing this one out to  me       ......just proves I shouldn't be too  hasty with my answers without thinking them through  !!!!

 

cool cool cool 

CPhill  Feb 5, 2021

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