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Math Help - Finding the Domain.

  1. #1
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    Finding the Domain.

    Find the domain: f(x) = log5(x - 7).
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  2. #2
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    Quote Originally Posted by garbles View Post
    Find the domain: f(x) = log5(x - 7).
    you can only take the log of positive values ... what does that tell you?
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  3. #3
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    that there is no solution?
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  4. #4
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    Quote Originally Posted by garbles View Post
    that there is no solution?
    If we cannot take the log of a negative number, then it means that the domain is all values that make the expression x-7 positive, because if x-7 is negative, the function is undefined.

    For your question, what Skeeter is saying is that the domain of your function is all the values of x for which we are not taking a logarithm of a negative number.

    If we have f(x)=log_{5}(x-7) then (x-7) > 0 for the function to be defined. so that is your domain. Can you take it from here an solve the inequality or do you need further clarification?
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    x >= 7?


    I put x > 7 but i dont understand why its x >= 7?
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    Quote Originally Posted by garbles View Post
    x >= 7?


    I put x > 7 but i dont understand why its x >= 7?
    sorry that was a typo on my part.
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  7. #7
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    Oh ok, so the answer is D : X > 7.

    but what if, f(x) = log5(x + 7). would the domain be, X > -7?
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  8. #8
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    Quote Originally Posted by garbles View Post
    Oh ok, so the answer is D : X > 7.

    but what if, f(x) = log5(x + 7). would the domain be, X > -7?
    That's right.

    The domain is the values of x for which f(x) is defined. When asked to find the domain of a function, I generally look for where the function is undefined, rather than finding where it is defined. For something like your question it's easy to see where it is undefined because logarithms not being able to be taken of negative numbers gives us an inequality and we can infer our domain from that.
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