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Thread: In Desperate need of help: How do I go about solving 3^{x^2 + x} = 9.

  1. #1

    In Desperate need of help: How do I go about solving 3^{x^2 + x} = 9.

    How do I go about solving 3x^2+x=9. Thanks in advance

  2. #2
    Elite Member mmm4444bot's Avatar
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    Hint: Write 9 as 3^2
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  3. #3
    Quote Originally Posted by mmm4444bot View Post
    Hint: Write 9 as 3^2
    Thank you, but Iím still confused as to what to do with having 2 x variables. Iím sorry if I sound stupid but Iím a new student and I have a terrible teacher. Thanks again

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    Elite Member mmm4444bot's Avatar
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    Let's get a new equation, first. After subsituting 3^2 for 9, we have this:

    3^(x^2 + x) = 3^2

    This equation shows two powers of 3 set equal to one another. Can you use a basic property of exponents, to write another equation where x does not appear in any exponents?
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  5. #5
    Quote Originally Posted by mmm4444bot View Post
    Let's get a new equation, first. After subsituting 3^2 for 9, we have this:

    3^(x^2 + x) = 3^2

    This equation shows two powers of 3 set equal to one another. Can you use a basic property of exponents, to write another equation where x does not appear in any exponents?
    So the answer would be x=1 right? My school uses an online system to do homework and itís telling me x=1 is wrong?

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    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by jedediahjamez View Post
    So the answer would be x=1 right?
    That's part of the answer.

    Did you write (and maybe solve) a new equation, as I suggested? If so, may I see the equation and your work?

    If you did not solve an equation, how did you get x = 1?
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  7. #7
    Elite Member mmm4444bot's Avatar
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    Here's the basic property of exponents that I have in mind:

    Given b^m = b^n, then m = n

    In other words, if two powers of the same base are equal, then the exponents must be equal. Here are some examples:

    14^2 = 14^z means z = 2

    A^(4y) = A^(y - 5) means 4y = y - 5

    (3/4)^(t^3/17) = (3/4)^(4t^5) means t^3/17 = 4t^5

    If you apply this property to the given equation in your exercise (after substituting 3^2 for 9), you'll get a basic quadratic equation to solve for x. (There are two solutions.)
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by jedediahjamez View Post
    So the answer would be x=1 right? My school uses an online system to do homework and itís telling me x=1 is wrong?
    Please reply showing how you followed through on the steps and hints you were provided. You created the equation they'd almost given you, you solved this using the Quadratic Formula, you got the two values, and... how did you get that "x=1" is the only answer?

    Please be complete. Thank you!

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    Quote Originally Posted by jedediahjamez View Post
    So the answer would be x=1 right? My school uses an online system to do homework and itís telling me x=1 is wrong?
    Well clearly x = 1 is NOT wrong.

    [tex]x = 1 \implies x = 1 \implies x^2 = 1 \implies x^2 + x = 1 + 1 = 2 \implies 3^{(x^2 +x)} = 3^2.[/tex]

    But x = 1 is not the ONLY correct answer. That is why the computer said you were wrong.

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