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Math Help - 2^(x)2^(x+1)2^(x+2)=2^6

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    2^(x)2^(x+1)2^(x+2)=2^6

    2^(x)2^(x+1)2^(x+2)=2^6

    Find all integers for the equation.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by techmath View Post
    2^(x)2^(x+1)2^(x+2)=2^6

    Find all integers for x the equation.
    By exponent properties, this is the same as 2^{x+x+1+x+2}=2^6\implies 2^{3x+3}=2^6. This now implies that 3x+3=6.

    Can you continue?
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    Quote Originally Posted by Chris L T521 View Post
    By exponent properties, this is the same as 2^{x+x+1+x+2}=2^6\implies 2^{3x+3}=2^6. This now implies that 3x+3=6.

    Can you continue?
    I am extremly sorry!

    it is supposed to be: 2^(x)+2^(x+1)+2^(x+2)=2^6
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  4. #4
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    Quote Originally Posted by techmath View Post
    I am extremly sorry!

    it is supposed to be: 2^(x)+2^(x+1)+2^(x+2)=2^6
    Factor by 2^x :
    2^x(1+2+4)=2^6

    7 \cdot 2^x=2^6

    7 divides the left hand side. Thus it has to divide the right hand side, which is not possible !

    So there is no positive solution to this equation.
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