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Math Help - Exponent and Log problem

  1. #1
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    Exponent and Log problem

    I have this one problem that I'm not sure how to start or end in solving for x.
    3^(3x-1)=2^(2x-1)
    I have tried taking the log of both sides but it just came out more complicated. Any help would be appreciated.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by NDHS View Post
    I have this one problem that I'm not sure how to start or end in solving for x.
    I have tried taking the log of both sides but it just came out more complicated. Any help would be appreciated.
    Taking logs of both sides here will make things much simpler...

    \ln3^{(3x-1)}=\ln2^{(2x-1)}

    Properties of logs allow us to puill the exponents out, like this
    (3x-1)\ln3=(2x-1)\ln2

    Now solve for x...
    Last edited by VonNemo19; January 1st 2010 at 06:42 PM.
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  3. #3
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    VonNemo19, group things in LaTex with { }. That is, 3^{3x-1} will give you 3^{3x-1}.
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  4. #4
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    Quote Originally Posted by NDHS View Post
    I have this one problem that I'm not sure how to start or end in solving for x.
    I have tried taking the log of both sides but it just came out more complicated. Any help would be appreciated.
    This is how I do it:

     3^{(3x-1)}=2^{(2x-1)}

     (3x-1)log3 = (2x-1)log2

    Now you have to expand them

     3xlog 3 - log 3 =  2xlog 2 - log 2

    Now you have to collect like terms

     3x log 3 - 2x log 2 = log 3 - log 2

    Factor out the greatest common factor

     x (3 log 3 - 2 log 2) = log 3 - log 2

    Now bring (3 log 3 - 2 log 2) over to the other side by canceling out so only x remains. You can do this by divinding it on both sides.

    So your exact answer is:

    x = (log 3 - log 2) over (3 log 3 - 2 log 2)

    Note: To cancel out a term or number. You have to do the opposite sign of what it is telling you to do to bring to the other side. For example. If you want to know all the ways that 2+3 = 5. You have to either subtract 2 or 3 on both sides to cancel it out on the left side to bring it to the right side.
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    VonNemo19, group things in LaTex with { }. That is, 3^{3x-1} will give you 3^{3x-1}.
    I'm working from a different PC as I am currently on vacation. The resolution is terrible. I thought that everything was honky dory.

    Thanks.
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