FInding domains of ln problems

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In summary, to find the domain of y=ln(6-x), you need to set 6-x greater than 0, which gives the domain as ]-inf;6[. The ln part is important because it determines the condition that the input should be over 0.
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Homework Statement



How do you find the domain of y=ln(6-x) ?


The Attempt at a Solution



do i have to set 6-x greater than or equal to 0 to then get that x is less than or equal to 6, or is there more to it than that? I'm confused on where the ln part comes in. Please assist.
 
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There isn't more to it, but you made a mistaking setting it to "or equal to zero", since zero is not in it's domain.
6-x>0 <--> 6>x
can also be written ]-inf;6[

The ln part is why we set condition that it is over 0, we need knowledge of the function to determine that.
 
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  • #3
just what i needed. thank you!
 

FAQ: FInding domains of ln problems

1. What is the domain of a natural logarithm function?

The domain of a natural logarithm function, ln(x), is all positive real numbers.

2. Can the natural logarithm function have negative inputs?

No, the natural logarithm function, ln(x), is only defined for positive real numbers. It is undefined for negative numbers and zero.

3. How do you find the domain of a natural logarithm function?

To find the domain of a natural logarithm function, you need to look for any restrictions on the input variable. If there are no restrictions, then the domain is all positive real numbers. If there are restrictions, such as a denominator cannot be equal to zero, then those values must be excluded from the domain.

4. Are there any special cases when finding the domain of a natural logarithm function?

Yes, there are two special cases when finding the domain of a natural logarithm function. The first is when the input variable is inside the logarithm. In this case, the input must be greater than zero. The second is when the natural logarithm function is inside another function. In this case, the entire input of the inner function must be greater than zero.

5. Can the domain of a natural logarithm function be extended beyond positive real numbers?

No, the natural logarithm function, ln(x), is only defined for positive real numbers. It cannot be extended to include negative numbers or complex numbers.

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