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Negative Solutions for x?

  1. Dec 7, 2004 #1
    K the question is 3^x^2+20=(1/27)^3x
    well I got 3^x^2+20=(3^-3)^3x
    the exponents make a quadratic function so i just set it = to 0 and factored to solve for x but this is what i got (x+4)(x+5) this means x=-4, or -5 but doesnt that mean there is no solution? We are not doing Log yet.
     
  2. jcsd
  3. Dec 7, 2004 #2

    Hurkyl

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    (don't forget parentheses when writing expressions)

    Okay... why?
     
  4. Dec 7, 2004 #3
    Ok i dont know because this question seemed similar to an example problem I had, this A one look below

    22x-2x=12 You can convert both sides of the equation to a common base; however, you can solve this exponential equation algebraically (without graphing calculator). Make sure you know how to solve this type of question algebraically.

    (2x)2-2x=12 apply law of exponent

    Now, if you take a close look, this equation looks like a quadratic equation. Let A be 2x, and rewrite the equation.

    A2-A=12

    A2-A-12=0

    (A+3) (A-4)=0

    A= -3 or A= 4

    Therefore, 2x= -3, or 2x= 4.

    The first equation, 2x= -3, has no solution since any positive base raised to any exponent results in a positive value.

    The second equation, 2x=4, gives:
    2x =22

    Therefore, x = 2.
     
  5. Dec 7, 2004 #4
    I did this problem wrong for sure can someone help me out plz :confused:
     
  6. Dec 7, 2004 #5

    dextercioby

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    I don't mean to be mean,but u have a MAJOR DISSRESPECT FOR THE NOTION OF PARANTHESIS.
    When writing down mathematical expressions,paranthesis mean a great deal,since u could get absurd results without taking them into consideration/interpreting the existing ones in a wrong way.
    Now,to answer your first post,since the second contained no question,the sollutions u found "x=-4",are and "x=-5" are pefect and more,are unique,and they both check the initial equation as u can easily check.
    Note that this time there's noi other equation of the kind "a^{x}=negative number",as in the example posted above.The negative numbers are just the sollution and they needn't be equalled to and exponential function.
    Anyway,i find awkward that u study exponential equations before logarithms,as most solutions of such equations can be given in terms of logarithms.
     
  7. Dec 7, 2004 #6
    X being negative does not make it a invalid solution, it's perfectly okay to have negative exponent values, the solutions are -4, -5.
     
  8. Dec 7, 2004 #7
    Thanks Nothing thats all I wanted to know. :smile:
     
  9. Dec 7, 2004 #8
    YES THANKYOU FOR UR COMMENTS AND HELP :grumpy:
     
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