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Math Help - Log's - Please Help

  1. #1
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    Log's - Please Help

    Hello, I have a question for you out their, please see attached file, i dont understand the question being asked off me, could someone explain it in plain english please.

    Any help would be greatly appriciated.

    Thanks
    Attached Thumbnails Attached Thumbnails Log's - Please Help-logs.jpg  
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, TheBigJ!

    Express the function \frac{a^2b^3}{100\sqrt{x}} in terms of \log_{10}(a),\;\log_{10}(b),\;\log_{10}(c)
    I'll omit the "subscript 10" . . .


    Let y \;=\;\frac{a^2b^3}{100\sqrt{c}}

    Take logs:

    . . \log(y) \;=\;\log\left(\frac{a^2b^3}{100\sqrt{c}}\right)

    . . \log(y)\;=\;\log(a^2b^3) - \log(100\sqrt{c})

    . . \log(y)\;= \;\log(a^2) + \log(b^3) - \bigg[\log(100) + \log(c^{\frac{1}{2}})\bigg]

    . . \log(y) \;=\;\log(a^2) + \log(b^3) - \log(100) - \log(c^{\frac{1}{2}})

    . . \log(y) \;=\;2\log(a) + 3\log(b) - 2 - \tfrac{1}{2}\log(c)


    Therefore: . y \;=\;\frac{a^2b^3}{100\sqrt{c}}  \;=\;10^{2\log(a) + 3\log(b) - 2 -\frac{1}{2}\log(c)}

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