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Math Help - Rearranging log equation 2

  1. #1
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    Rearranging log equation 2

    How do I rearrange this for y?

    log(10)y=3log(10)x+2

    thx
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  2. #2
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    Re: Rearranging log equation 2

    In fact what you want is not clear
    It may be written as
    log 10y - 3 lof 10x = 2
    log (10y)/( 1000 x ^3) = 2
    If the log is to the base 10 then we have
    (10y)/( 1000 x ^3) = 10 ^ 2 etc please be specific with your question so as to enable us to help and avoid guess work
    Thanks from JellyOnion and topsquark
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  3. #3
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    Re: Rearranging log equation 2

    Sorry I didn't realise.
    I did mean base 10 thx
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  4. #4
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    Re: Rearranging log equation 2

    log(y/x^3)=10^2
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  5. #5
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    Re: Rearranging log equation 2

    Recall that y= 10^{log(y)}. Does this give you any ideas how to simplify the LHS?

    -Dan
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  6. #6
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    Re: Rearranging log equation 2

    Hello, JellyOnion!

    Since the base is 10 (ten), we can drop the subscript.


    \text{Solve for }y\!:\;\log y \:=\:3\log x+2

    We have: . \log y \;=\; 3\log x + 2\cdot 1 \;=\;3\log x + 2\log(10)

    . . . . . . . . \log y \;=\;\log(x^3) + \log(10^2) \;=\;\log(x^3) + \log(100)

    . . . . . . . . \log y \;=\;\log(100x^3)

    Therefore:. . . y \;=\;100x^3
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  7. #7
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    Re: Rearranging log equation 2

    Or log(y)= 3log(x)+ 2 so log(y)- 3 log(x)= log(y/x^3)= 2
    y/x^3= 100, y= 100x^3
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  8. #8
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    Re: Rearranging log equation 2

    Thank u everyone, much appreaciated
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