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Math Help - Log or ln

  1. #1
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    Log or ln

    My problem is 2^3x=3^x+4

    i have been trying this problem and have done or gotten this far.. i dont know if its right or wrong but....


    3x ln2= x+4 ln3

    3 ln2 + x ln2 = x ln 3 + 4 ln 3

    x ln 2 - x ln 3 = 4 ln 3 - 3 ln 2

    x ln 2/3 = ? ln 3/2

    this is what i got and im stumped am i on the right track and or what is the next step..

    any help is appreciated
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  2. #2
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    Re: Log or ln

    \displaystyle x (\ln 2 - x \ln 3) = 4 \ln 3 - 3 \ln 2

    \displaystyle x  = \frac{4 \ln 3 - 3 \ln 2}{\ln 2 - x \ln 3}

    And that's it!
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  3. #3
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    Re: Log or ln

    2^(3x) = 3^(x+4)
    taking log on both sides we get
    3x log 2 = ( x+4) log 3
    3xlog2 - xlog 3 = 4log 3
    x[ 3log 2 - log 3] = 4 log 3
    x log ( 8/3) = 4log 3
    Now you can workout the value of x
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  4. #4
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    Re: Log or ln

    Quote Originally Posted by gramgilb View Post
    My problem is 2^3x=3^x+4

    i have been trying this problem and have done or gotten this far.. i dont know if its right or wrong but....


    3x ln2= x+4 ln3

    3 ln2 + x ln2 = x ln 3 + 4 ln 3

    x ln 2 - x ln 3 = 4 ln 3 - 3 ln 2

    x ln 2/3 = ? ln 3/2

    this is what i got and im stumped am i on the right track and or what is the next step..

    any help is appreciated
    What you have posted is meaningless; If you are going to post in ASCII learn to use parentheses to make your expressions unambiguous.

    The helpers have assumed you mean:

    2^{3x}=3^{x+4}

    which is not unreasonable given what follows, but that is not what you have posted means under the usual conventions which may be:

    2^{3x}=3^x +4

    or even

    2^3 x=3^x+4

    etc..

    .
    Thanks from MarkFL
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  5. #5
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    Re: Log or ln

    Quote Originally Posted by zzephod View Post
    What you have posted is meaningless; If you are going to post in ASCII learn to use parentheses to make your expressions unambiguous.

    The helpers have assumed you mean:

    2^{3x}=3^{x+4}

    which is not unreasonable given what follows, but that is not what you have posted means under the usual conventions which may be:

    2^{3x}=3^x +4

    or even

    2^3 x=3^x+4

    etc..

    .
    K sorry didnt know that but will learn to do that for any other inquiries

    thank you
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