Domain of the Function f(x): Explained

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SUMMARY

The domain of the function f(x) = log5(log5(x + 2)) is definitively (-1, ∞). This conclusion arises from the requirement that both the inner and outer logarithmic functions must have positive inputs. Specifically, x + 2 must be greater than 0, leading to x > -2, and log5(x + 2) must also be greater than 0, resulting in x + 2 > 1, or x > -1. Thus, the correct domain is (-1, ∞).

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the_storm
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The Question is: What is the Domain of the function f(x)= log_{5}(log_{5}(x + 2)
My answer is that the Domain is (-2, \infty). However the it is said that the right answer is (-1, \infty) and I am not convinced so can anyone give me an explanation?
 
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You can't take logs of negative numbers. So you'll need to make sure that

x+2\geq 0

But there's another log in that formula. That log also can't take negatives as input. So moreover, you'll have to make sure that

\log^5(x+2)\geq 0
 
so Domain is (-1, infinty) right??
 
Yes!
 
Just nitpicking to pass the morning. It's not just negative numbers you can't take the log of. It's also zero. You can't take the log of a non-positive number. No?
 
You cannot take the log of zero.
 
If we are nitpicking: "the domain" of a function is part of the definition of that function. OP is asking for the largest possible domain that is compatible with the given formula.
 
It's true Landau, but nobody disputed that.
 
can you be more explicit
 

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