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Math Help - Am I right?

  1. #1
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    Am I right?

    The question is:
    State the domain of the function f(x) = log3 (x - 4)

    I believe that the answer is all real number except 4.
    Is this correct?
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by iluvmathbutitshard View Post
    The question is:
    State the domain of the function f(x) = log3 (x - 4)

    I believe that the answer is all real number except 4.
    Is this correct?
    Nope try again.

    It would be (4,\infty)
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  3. #3
    Junior Member
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    Quote Originally Posted by iluvmathbutitshard View Post
    I believe that the answer is all real number except 4.Is this correct?
    You have to remember that.....

    \log_a{b} = x \rightarrow a^{x} = b

    Then think about what a^{x} will give me a negative number for b....none. You might think -1 or -2, but those are merely a^{-1} = \frac{1}{a} and a^{-2} = \frac{1}{a^{2}} and so on and so forth.

    Similarly no x value will also give you 0, some might try zero, but a^{0} = 1

    So you can see that the domain has to be restricted for positive values.

    An easy way to find what values will work is

    x - 4 > 0 and solve. Remember it cannot be 0 so it's a strict inequality.

    If you are given numerous logs you can do the same for each and if you end up with a quadratic you can compare the solutions to see which fit the criteria.

    Hopefully this helps.
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  4. #4
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    Smile

    Quote Originally Posted by iluvmathbutitshard View Post
    The question is:
    State the domain of the function f(x) = log3 (x - 4)

    I believe that the answer is all real number except 4.
    Is this correct?
    no,the logarithm function is defined only in \mathbb{R}^{+} ^{*}
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