Math 10

EXPONENTIAL EQUATION

Find the X

3^x - 82/9 = -3^-x

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  1. 3^x + 3^-x = 82/9
    3^x + 1/3^x = 82/9
    (3^2x + 1)/3^x = 82/9
    clearly, x=2, but let's go on.
    9(3^2x + 1) = 82*3^x
    9*3^2x - 82*3^x + 9 = 0
    think of this as 9u^2-82u+9, and you get
    (9*3^x - 1)(3^x - 9) = 0
    3^x = 9 or 1/9
    x = 2 or -2
    aha. an unexpected solution!

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  2. Thank you so much. It really helps me 😂

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