Domain of logarithmic funtion

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Homework Help Overview

The discussion revolves around determining the domain of a logarithmic function, specifically focusing on the expression involving a logarithm in the denominator. Participants are exploring the conditions under which the function is defined.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to identify the domain by setting conditions for the logarithmic function and its denominator. Questions arise regarding the exclusion of certain values, particularly the number 12, and the implications of having a logarithm equal to 1 in the denominator.

Discussion Status

The discussion is active, with participants providing hints and engaging in clarifying questions. There is a focus on understanding why certain values are excluded from the domain, particularly through the exploration of the logarithmic properties and their impact on the function's definition.

Contextual Notes

Participants are navigating the constraints of logarithmic functions, particularly regarding the conditions that lead to undefined expressions, such as division by zero.

lwelch70
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6throute (x-7)
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log11(13-x)


What is the domain of the function in interval notation.


I know to set x-7 > 0, so that gets me x>7 , and I know I have to set 13-x > 0, which gets me x < 13. But the notation that is correct is [7,12)U(12,13). Where do you get the 12 from?
 
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Hi lwelch70! :smile:

(have a ≥ :wink:)
lwelch70 said:
But the notation that is correct is [7,12)U(12,13). Where do you get the 12 from?

Hint: what's 1/log11(13 - 12) ? :wink:
 
tiny-tim said:
Hi lwelch70! :smile:

(have a ≥ :wink:)


Hint: what's 1/log11(13 - 12) ? :wink:


I'm sorry but that just confused me. Haha.
 
Is it because it's in the denominator? So I won't be able to take the log of any base of 1 since that would give me 0 as a denominator?
 
[STRIKE]Well, the answer, [7,12)U(12,13), excludes the value 12 …

so pop it into the formula to see why! :smile:[/STRIKE]

oops, you beat me to it! :biggrin:

Yes, you can't have something/0 :smile:
 
So if I would see this on a test, and am not given the correct answer (haha), I simply make surre that I am not taking log(anything that equals 1) in the denominator?
 
That's it! :smile:
 

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