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Math Help - Logarithmic Equation Explaination

  1. #1
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    Logarithmic Equation Explaination

    I'm having a difficult time with this problem because I'm not understnading how to implement the properties to this problem. Is there someone how would be willing to explain the process to me. Please!

    Here is the equation,

    3 logx = 3x (the (logx) is the exponent)



    You help is much appreciated.

    Aaron
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello
    Quote Originally Posted by ih8mathes View Post
    I'm having a difficult time with this problem because I'm not understnading how to implement the properties to this problem. Is there someone how would be willing to explain the process to me. Please!

    Here is the equation,

    3 logx = 3x (the (logx) is the exponent)
    3^{\log x}=3x \Longleftrightarrow \log\left( 3^{\log x}\right)=\log\left(3x \right)

    Using the properties of the natural logarithm you should be able to solve this for x.
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  3. #3
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    Match answer

    I got x=1 is that right?
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by ih8mathes View Post
    I got x=1 is that right?
    No. 3^{\log 1}=3^0=1 doesn't equal 3\times 1=3. Can you show us what you've done to find x=1 ?
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  5. #5
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    Quote Originally Posted by flyingsquirrel View Post
    Hello


    3^{\log x}=3x \Longleftrightarrow \log\left( 3^{\log x}\right)=\log\left(3x \right)

    Using the properties of the natural logarithm you should be able to solve this for x.
    Quote Originally Posted by ih8mathes at a thread that should be deleted soon View Post
    I've inquired about this previously and don;t mean to bother with it again, but I've pulled all of my hair out trying to figure this equation out only to be told I've missed a step. Could someone please show me how to solve for x in this equation?



    3^logx=3x



    I'm looking for a step by step process to solving this equation please. Thanks for you help.

    Aaron
    Following from flyingsquirrel:

    \Rightarrow (\log x) (\log 3) = (\log 3) + (\log x)

    \Rightarrow \log x (\log 3 - 1) = \log 3

    \Rightarrow \log x = \, ....

    \Rightarrow x = \, ....
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  6. #6
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    Quote Originally Posted by flyingsquirrel View Post
    Hello


    3^{\log x}=3x \Longleftrightarrow \log\left( 3^{\log x}\right)=\log\left(3x \right)

    Using the properties of the natural logarithm you should be able to solve this for x.
    Taking over from here:
    log \left ( 3^{log(x)} \right ) = log(3x)

    (log(x)) \cdot log(3) = log(3) + log(x)

    Let y = log(x). Then this is
    y \cdot log(3) = log(3) + y

    Solve this for y. Then how do you find x from this?

    -Dan
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