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Math Help - please help in exponential simultaneous equation

  1. #1
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    Question please help in exponential simultaneous equation

    Need help in solving this simultaneous equations:
    from add maths book by Ho Soo Thong
    (64) (4^y) = 16^x -------eq 1 (I have already reduced it to y=2x-3)

    3^y = 4[3^(x-2)] - 1 --------eq 2


    Have tried many different ways but to no avail. Kindly help
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  2. #2
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    Quote Originally Posted by mbasit View Post
    Need help in solving this simultaneous equations:
    from add maths book by Ho Soo Thong
    (64) (4^y) = 16^x -------eq 1 (I have already reduced it to y=2x-3)

    3^y = 4[3^(x-2)] - 1 --------eq 2


    Have tried many different ways but to no avail. Kindly help
    Substitute y by 2x - 3 in the 2nd equation:

    3^y=4 \cdot 3^{x-2} - 1

    3^{2x-3}=4 \cdot 3^{x-2} - 1

    \dfrac{3^{2x}}{27}=\dfrac49 \cdot 3^x - 1 Multiply by 27

    3^{2x}-12 \cdot 3^x+27=0

    This is a quadratic equation in 3^x. Substitute z = 3^x

    z^2-12z+27=0~\implies~z = 3~\vee~z = 9

    Resubstitute to get x = 2 or x = 1
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