Domain of logarithmic funtion

[lwelch70]

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?

 

[tiny-tim]

Hi lwelch70!

(have a ≥ )

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) ?

 

[lwelch70]

Hi lwelch70!

(have a ≥ )


Hint: what's 1/log₁₁(13 - 12) ?

I'm sorry but that just confused me. Haha.

 

[lwelch70]

Is it becuase 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?

 

[tiny-tim]

[STRIKE]Well, the answer, [7,12)U(12,13), excludes the value 12 …

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

oops, you beat me to it!

Yes, you can't have something/0

 

[lwelch70]

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?

 

[tiny-tim]

That's it!