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C2 Maths Help with exponentials and logarithms watch

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    Stuck on this C2 question not sure what to do, just want someone to give me an idea on how to do each question.
    The roots of the equation 2log(base"4")x-log(base"4")(7x-3) = -1/2 are Alpha and Beta where Alpha < Beta

    a. Find Alpha and Beta and show that log(base"4")alpha = -1/2

    b. Calculate log(base"4")Beta to 3 significant figures

    Any help with these questions is much appreciated
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    (Original post by washdog)
    Stuck on this C2 question not sure what to do, just want someone to give me an idea on how to do each question.
    The roots of the equation 2log(base"4")x-log(base"4")(7x-3) = -1/2 are Alpha and Beta where Alpha < Beta

    a. Find Alpha and Beta and show that log(base"4")alpha = -1/2

    b. Calculate log(base"4")Beta to 3 significant figures

    Any help with these questions is much appreciated
    What have you tried?
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    (Original post by washdog)
    Stuck on this C2 question not sure what to do, just want someone to give me an idea on how to do each question.
    The roots of the equation 2log(base"4")x-log(base"4")(7x-3) = -1/2 are Alpha and Beta where Alpha < Beta

    a. Find Alpha and Beta and show that log(base"4")alpha = -1/2

    b. Calculate log(base"4")Beta to 3 significant figures

    Any help with these questions is much appreciated
    They both have the same base, so you can use your standard rules. What can you do to combine the two log terms into a single term?
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    remember 2logx = logx^2

    try and remove the log's to get a quadratic equation
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    try Goods`s suggestion, and collect the logs using:

    log_{4}a-log_{4}b=log_{4}(\frac{a}{b}) for the LHS,

    then you can simplify what you get using:

    log_{4}(\frac{a}{b})=RHS=&gt;4^{RHS  }=\frac{a}{b}

    you get the quadratic from this.
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    When i simplified i got 1/2 = x^2/7x-3 What do i do next times by 7x-3?
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    multiply both sides by 2(7x-3) to get: 7x-3=2x^2 re-arrange to get: 2x^2-7x+3=0, solve quadratic.
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    the statement in A) actually tells you what one of the roots is, because its` basically saying that:

    4^{-1/2}=x_1 where x_1 is one of the roots

    b) you can get by converting the log staatement to one in natural logs:

    \displaystyle \frac{ln(x_{2})}{ln(4)}
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    I got 1/2 and 3 to be the roots which is the right answer and when putting 1/2 in i get -1/2 Thanks for the help guys much appreciated
 
 
 
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