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Thread: Domain of natural log

  1. #1
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    Domain of natural log

    find the domain of the function

    f(x) = ln(1/x-10)

    i set the equation to f(x)= Ln1-Lnx-10

    then i dont know, same as below

    f(x) = log base10 [(x+2)/(x-3)]
    f(x)= log base 10^x+2 - log base 10^x-3

  2. #2
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    Re: Domain of natural log

    Quote Originally Posted by alyren
    find the domain of the function

    f(x) = ln(1/x-10)

    i set the equation to f(x)= Ln1-Lnx-10

    then i dont know, same as below

    f(x) = log base10 [(x+2)/(x-3)]
    f(x)= log base 10^x+2 - log base 10^x-3
    First tell us what is the domain of:

    f(x) = ln(x)
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
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    Re: Domain of natural log

    would that be all real numbers,except 10?

  4. #4
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    Re: Domain of natural log

    Quote Originally Posted by alyren
    would that be all real numbers,except 10?
    what is the domain of:

    f(x) = ln(x)

    It would be x > 0 [meaning all the real numbers greater than 0]

    So in your case {f(x) = ln [1/(x-10)]} the domain is (x - 10) > 0
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  5. #5
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    Re: Domain of natural log

    what about the (1/x-10),
    x can't equal to 10?

    can you show me step to solve it?

  6. #6
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by alyren

    f(x) = ln(1/x-10)

    Your typing means this:

    [tex]f(x) \;=\; ln \left ( \frac{1}{x} \;-\; 10 \right )[/tex]

    Is that what you intend ?

    i set the equation to f(x)= Ln1-Lnx-10

    ln(1) - ln(x) - 10 does not equal ln(1/x - 10)
    Maybe function f is defined this way:

    [tex]f(x) \;=\; ln \left ( \frac{1}{x - 10} \right )[/tex]

    If so, then we show the denominator by typing grouping symbols.

    f(x) = ln(1/[x - 10])

    Then you can write:

    f(x) = ln(1) - ln(x - 10)

    This can be simplified because ln(1) is a constant.

    Do you know? Subtracting 10 from x causes the graph to shift 10 units to the right.

    If you're familiar with the graph and domain of ln(x), then the graph and domain of ln(x - 10) should be clear to you.

    If you're not familiar with the graph and domain of ln(x), then perhaps you are not ready for this exercise.

    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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