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Math Help - Logarithmic expressions

  1. #1
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    Logarithmic expressions

    Hi, I need help with the following question in the attachment. It is about logs, I don't understand this problem. Please help, thanks in advanced
    Attached Thumbnails Attached Thumbnails Logarithmic expressions-capture.jpg  
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  2. #2
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    Re: Logarithmic expressions

    Note that \log_8 {64} = 2. Also, \log_8 {64} = 3 \log_8 {4} by a logarithmic identity. Therefore


    3 \log_8 {4} = 2 \Rightarrow \log_8 {4} = \frac{2}{3}.
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  3. #3
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    Re: Logarithmic expressions

    There is no exponent 3 though. How did you end up with log64 base 8?
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  4. #4
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    Re: Logarithmic expressions

    I'm using 64 because 64 = 4^3 = 8^2.
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  5. #5
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    Re: Logarithmic expressions

    Quote Originally Posted by dan713 View Post
    Hi, I need help with the following question in the attachment. It is about logs, I don't understand this problem. Please help, thanks in advanced
    Here is another way to look at it.
    x = {\log _8}(4)\; \Rightarrow {8^x} = 4\; \Rightarrow \;x = \frac{2}{3}.
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  6. #6
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    Re: Logarithmic expressions

    Quote Originally Posted by Plato View Post
    Here is another way to look at it.
    x = {\log _8}(4)\; \Rightarrow {8^x} = 4\; \Rightarrow \;x = \frac{2}{3}.
    That is correct but it might not be immediately apparent to dan713 that x = 2/3. Unless you note that \sqrt[3]{8^2} = 4, or you write it as 2^{3x} = 2^2.
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