# Domain of logarithmic funtion

• lwelch70
In summary, the domain of the given function in interval notation is [7,12)U(12,13). The value of 12 is excluded because it results in a denominator of 0 when plugged into the formula. Therefore, it is important to not take the logarithm of a value that equals 1 in the denominator when solving for the domain.
lwelch70
6throute (x-7)
--------------
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?

Hi lwelch70!

(have a ≥ )
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) ?

tiny-tim said:
Hi lwelch70!

(have a ≥ )

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

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

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?

[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

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!

## 1. What is a logarithmic function?

A logarithmic function is a type of mathematical function that represents the inverse relationship between exponentiation and logarithms. It is written in the form of f(x) = logb(x), where b is the base of the logarithm and x is the input value.

## 2. What is the domain of a logarithmic function?

The domain of a logarithmic function is all the possible input values (x) for which the function is defined. In other words, it is the set of all real numbers greater than 0, as the logarithm of 0 and negative numbers is undefined.

## 3. How do you find the domain of a logarithmic function?

To find the domain of a logarithmic function, set the argument of the logarithm (x) greater than 0 and solve for x. This will give you the range of values that x can take for the function to be defined.

## 4. Can the domain of a logarithmic function be negative?

No, the domain of a logarithmic function cannot be negative. As mentioned earlier, the logarithm of 0 and negative numbers is undefined, so the domain must be restricted to positive values.

## 5. What happens if the base of a logarithmic function is 1?

If the base of a logarithmic function is 1, then the function becomes f(x) = log1(x), which is undefined. This is because any number raised to the power of 0 is equal to 1, so there is no unique solution for the input value x.

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