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Math Help - Equation

  1. #1
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    Equation

    Solve the equation 2|3^x-1|=3^x . giving your answsers to 3 sig figures.
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  2. #2
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    Re: Equation

    Quote Originally Posted by Matt512 View Post
    Solve the equation 2|3^x-1|=3^x . giving your answsers to 3 sig figures.
    first let's assume that $|3^x-1|\geq 0$

    then we solve

    $2(3^x-1)=3^x$

    Spoiler:
    $2\cdot 3^x - 2 = 3^x$

    $3^x = 2$

    $x = \log_3(2) = 0.631$


    Now if we assume $|3^x-1|\leq 0$

    we solve

    $2(1-3^x)=3^x$

    Spoiler:
    $2-2\cdot 3^x = 3^x$

    $2 = 3\cdot 3^x=3^{x+1}$

    $\log_3(2)=x+1$

    $x=\log_3(2)-1=-0.369$

    so $x=0.631$ OR $x=-0.369$
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  3. #3
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    Re: Equation

    Great thank you
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