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Math Help - Logarithm Problem

  1. #1
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    Logarithm Problem

    Hi,

    Please could anyone help with this problem please? I know the answers from an answer sheet (x=1 and x=ln12/ln4) , but I have no idea how the answers were reached.

    Many thanks


    4^2x + 48 = 4^(x+2)
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  2. #2
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    Re: Logarithm Problem

    Quote Originally Posted by runrun View Post
    Hi,

    Please could anyone help with this problem please? I know the answers from an answer sheet (x=1 and x=ln12/ln4) , but I have no idea how the answers were reached.

    Many thanks


    4^2x + 48 = 4^(x+2)
    4^{2x} + 48 = 4^{x+2}

    4^{2x} - 4^{x+2} + 48 = 0

    4^{2x} - 4^2 \cdot 4^x + 48 = 0

    (4^x)^2 - 16 \cdot 4^x + 48 = 0

    let u = 4^x ...

    u^2 - 16x + 48 = 0

    solve the quadratic for u by factoring ... then solve for x
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