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Math Help - Domain of e function

  1. #1
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    Domain of e function

    How do I find the domain of
     <br />
y=\sqrt{e^{5x}-2}<br />


    I have a test in a few hours so thanks for any help I can get!
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  2. #2
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    Can you have negatives inside a radical?

    What values of x cause the argument of the radical to be zero or greater?

    This will be your domain.
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  3. #3
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    Hello, lil_cookie!

    How do I find the domain of: .  <br />
y\:=\:\sqrt{e^{5x}-2}

    The radicand must be nonnegative.

    . . e^{5x} - 2 \:\geq \:0

    . . . . . e^{5x} \:\geq \:2

    . . . . . 5x \:\geq \:\ln 2

    . . . . . x \:\geq \:\tfrac{1}{5}\ln2

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  4. #4
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    Thank you!

    Here is another one:

    log_{4}+log_{4}(3x+11)=1
    x(3x+11)=4
    3x^{2}+11x-4=0
    I get x=1 and x=-11

    The q is to find all solutions
    Is this correct, or did I go wrong?
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  5. #5
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    Quote Originally Posted by lil_cookie View Post
    Thank you!

    Here is another one:

    log_{4}+log_{4}(3x+11)=1
    x(3x+11)=4
    3x^{2}+11x-4=0
    I get x=1 and x=-11

    The q is to find all solutions
    Is this correct, or did I go wrong?
    You didn't solve the quadratic correctly - use the quadratic formula to solve.

    Also log terms must be greater than 0 so the domain is x > -\frac{11}{3}
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  6. #6
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    Yes I was thinking I should have used the quad formula....thank you so much
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  7. #7
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    Quote Originally Posted by lil_cookie View Post
    Here is another one:

    log_{4}+log_{4}(3x+11)=1
    What is the argument of the first logarithmic term?
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