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MATH

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Determine the exact value of x.

a. 3^2x = 5(3^x) +36
b. (1/8)^x-3 = 2x16^2x+1
c. 3^x2 + 20 = (1/27)^3X

  • MATH - ,

    a) let 3^x = y
    so you have y^2 - 5y - 36=0
    (y-9)(y+4) = 0
    y = 9 or y = -4

    3^x = 9
    3^x = 3^2
    x = 2

    or 3^x = -4 , not possible

    b) the trick here is to see that all bases are powers of 2
    1/8 = 2^-3
    16 = 2^4

    so (1/8)^(x-3) = 2x16^(2x+1)
    (2^-3)^(x-3) = 2(2^4)^(2x+1)
    2^(-3x+9) = 2(2)^(8x+4)
    2^(-3x+9) = 2^(8x+5)
    then
    -3x+9 = 8x+5
    you can finish it ...

    c) I see no easy way to do this one.
    Why is the a capital X ?

  • MATH - ,

    Thank you for the help,
    I'm really stuck on c. The x was made capital by mistake, it's actually supposed to be lower case.

  • MATH - ,

    The equation is actually 3^x^2 + 20 = (1/27)^3x

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