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Math Help - logs past paper question

  1. #1
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    logs past paper question

    log2 x = log 4x +6
    this is a question my teacher gave us, the she gave this the first equation on starting the question which is below

    log2x = log2x +6 / log24

    how did my teacher got this, i need to know because i am presently studing for an exam

    PS the 2 and 4 is subscrip SORRY AND final log24 only the 2 is subscript
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  2. #2
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    Re: logs past paper question

    Quote Originally Posted by mathkid12 View Post
    log2 x = log 4x +6
    this is a question my teacher gave us, the she gave this the first equation on starting the question which is below

    log2x = log2x +6 / log24

    how did my teacher got this, i need to know because i am presently studing for an exam

    PS the 2 and 4 is subscrip SORRY AND final log24 only the 2 is subscript
    1. You can convert logs of a certain base into logs of another base by using:

    \log_a(b)=\frac{\log_c(b)}{\log_c(a)}

    2. Re-write the given equation:

    \log_2(x)=\log_4(x)+6~\implies~ \\ \log_2(x)=\frac{\log_2(x)}{\log_2(4)}+6~\implies~ \\ \log_2(x)=\frac{\log_2(x)}{2}+6

    3. Collect like terms:

    \frac12 \log_2(x)=6~\implies~\log_2(x)=12~\implies~x=2^{12  }=4096
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