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Math Help - Solve for x?

  1. #1
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    Solve for x?

    Solve for x:
    16^3x-2=(1/32)^2x-16

    How to start this?

    Thanks in advance.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Solve for x?

    A good place to start would be to restate the problem using bracketing symbols to let us know what the exponents actually are.
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  3. #3
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    Re: Solve for x?

    Hello, maiden129!

    Solve for x: 16^3x-2=(1/32)^2x-16

    If that equation is: . 16^{3x} -2 \:=\:\left(\tfrac{1}{32}\right)^{2x} - 16

    we have: . (2^4)^{3x} \:=\:(2^{-5})^{2x} - 14  \quad\Rightarrow\quad 2^{12x} \:=\:2^{-10x} - 14

    . . . . . . . . 2^{12x} + 14 - 2^{-10x} \:=\:0


    Multiply by 2^{10x}\!\!:\;\;2^{22x} + 14\cdot 2^{10x} + 1 \;=\;0

    Good luck!


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    If the equation is: . 16^{3x-2} \:=\:\left(\tfrac{1}{32}\right)^{2x-16}

    we have: . (2^4)^{3x-2} \:=\:(2^{-5})^{2x-16} \quad\Rightarrow\quad 2^{12x-8} \:=\:2^{-10x+80}


    Therefore: . 12x - 8 \:=\:-10x + 80 \quad\Rightarrow\quad 22x \:=\:88 \quad\Rightarrow\quad x \:=\:4
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