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Math Help - Examination questions

  1. #1
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    Exclamation Examination questions

    i can't solve this question

    if 5^x x 25^2y=1 and 3^5x x 9^y = 1/9 calculate the value of x and y
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  2. #2
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    Can you confrim this to be the system?

    5^{x} \times 25^{2y}=1

     3^{5x} \times 9^{y} = \frac{1}{9}
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  3. #3
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    yeah
    how did you do that?
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  4. #4
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    I made the equations look all pretty using LaTeX. For further information look at

    http://www.mathhelpforum.com/math-he...-tutorial.html

    I'll kick this off for you.

     5^{x} \times 25^{2y}=1 ....(1)

     3^{5x} \times 9^{y} = \frac{1}{9} ....(2)

    Let's have a look at (1)

     5^{x} =25^{-2y}

     5^{x} =(5^2)^{-2y}

     5^{x} =(5^2)^{-2y}

     5^{x} =5^{-4y}

     x= -4y

    Aim to do the same thing with (2) and you should find a solution.
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  5. #5
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    here's another way to do that (actually harder- pickslide's method is more fundamental and better):

    Given 5^x25^y= 1 and 3^{5x}9^y= 1, take logarithms of both sides (to any base). log(5^x)+ log(25^y)= log(x) or xlog(25)+ ylog(25)= 0 and since [tex]log(25)= log(5^2)= 2log(5)[tex], x log(5)+ 2y log(5)= 0 and, dividing both sides by log(25), x+ 2y= 0.

    Similarly, taking logarithms of both sides of 3^{5x}9^y= 1, 5x log(3)+ y log(9)= 5x log(3)+ 2y log(3)= 0 so 5x+ 2y= 0. And it should be pretty obvious that x= 0, y= 0 is the only solution to that.

    To see the "Latex" code for 5^x25^y= 1 and 3^{5x}9^y= 1, click on the formulas.
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