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Math Help - Given 2^x=8^(y+1)...

  1. #1
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    Given 2^x=8^(y+1)...

    Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.
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  2. #2
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    Quote Originally Posted by ceasar_19134 View Post
    Given 2^x=8^(y+1) and 9^y=3^(x-9), find the value of x+7.
    Your equations reduce.
    2^x = 8^(y+1) is 2^x = 2^(3y+3) or x=3y+3.
    9^y=3^(x-9) is 3^(2y) = 3^(x-9) or 2y=x-9.
    Now solve that system.
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  3. #3
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    2^x = 8^(y+1) is 2^x = 2^(3y+3) ---> x=3y+3.....(1)
    9^y=3^(x-9) is 3^(2y) = 3^(x-9) ---> 2y=x-9......(2)

    (x-3)/3 = y

    substitute this into (2)

    (2x - 6)/3 = x - 9
    2x - 6 = 3x - 27
    x = 21 (and y = 6)
    therefore
    x+7 = 28 -------> answer

    we can check the value of x is correct by resubstitution

    2^21 = 8^(7) = 2 097 152.
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