Domain of the Function f(x): Explained

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Discussion Overview

The discussion revolves around determining the domain of the function f(x) = log5(log5(x + 2)). Participants explore the conditions under which the logarithmic function is defined, particularly focusing on the implications of taking logarithms of negative numbers and zero.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant claims the domain is (-2, ∞), while another asserts it is (-1, ∞), expressing uncertainty about the correct answer.
  • Several participants note that logarithms cannot be taken of negative numbers or zero, which leads to the requirement that x + 2 must be greater than or equal to zero.
  • It is emphasized that the inner logarithm must also be non-negative, leading to the condition log5(x + 2) ≥ 0.
  • One participant points out that the definition of the domain is integral to the function itself and seeks clarification on the largest possible domain compatible with the formula.

Areas of Agreement / Disagreement

There is disagreement regarding the correct domain of the function, with some participants supporting (-1, ∞) and others suggesting (-2, ∞). The discussion remains unresolved as participants express differing interpretations of the conditions for the domain.

Contextual Notes

Participants highlight the importance of considering both the outer and inner logarithmic functions when determining the domain, but the specific assumptions and definitions used in their reasoning are not fully articulated.

the_storm
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The Question is: What is the Domain of the function f(x)= log[tex]_{5}[/tex](log[tex]_{5}[/tex](x + 2)
My answer is that the Domain is (-2, [tex]\infty[/tex]). However the it is said that the right answer is (-1, [tex]\infty[/tex]) 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

[tex]x+2\geq 0[/tex]

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

[tex]\log^5(x+2)\geq 0[/tex]
 
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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