Results 1 to 10 of 10

Math Help - Solving a logarithm equation

  1. #1
    Junior Member
    Joined
    May 2006
    Posts
    37

    Solving a logarithm equation

    How do you find x in terms of A for this equation

    2x+1=xlogA
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by kingkaisai2
    How do you find x in terms of A for this equation

    2x+1=xlogA
    You have to isolate the x, of course.

    2x +1 = xLogA
    Divide both sides by x,
    (2x +1)/x = LogA
    2x/x +1/x = LogA
    2 +1/x = LogA
    1/x = LogA -2
    Since Log(10) = 1, then,
    1/x = LogA -2Log(10)
    1/x = LogA -Log(10^2)
    1/x = LogA -Log(100)
    1/x = Log(A/100)
    1/x = Log(0.01A)
    Take the reciprocals of both sides,
    x = 1 / Log(0.01A) -------------------------answer.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ticbol
    You have to isolate the x, of course.

    2x +1 = xLogA
    Divide both sides by x,
    (2x +1)/x = LogA
    2x/x +1/x = LogA
    2 +1/x = LogA
    1/x = LogA -2
    Since Log(10) = 1, then,
    1/x = LogA -2Log(10)
    1/x = LogA -Log(10^2)
    1/x = LogA -Log(100)
    1/x = Log(A/100)
    1/x = Log(0.01A)
    Take the reciprocals of both sides,
    x = 1 / Log(0.01A) -------------------------answer.
    Except you have assumed that \log denotes log to the base
    10, which it may or may not do. But as this post is in the
    College/University Level Math forum it would be safer to assume
    natural logarithms.

    It would be best not to assume anything about the base of logarithms intended,
    it is probably clear to the original poster, but may not be obvious at second
    hand.


    RonL
    Last edited by CaptainBlack; May 22nd 2006 at 03:29 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by CaptainBlack
    Except you have assumed that \log denotes log to the base
    10, which it may or may not do. But as this post is in the
    College/University Level Math forum it would be safer to assume
    natural logarithms.

    It would be best not to assume anything about the base of logarithms intended,
    it is probably clear to the original poster, but may not be obvious at second
    hand.


    RonL
    log is log to the base ten
    ln is natural log, or log to the base e.
    I do not assume. That's what they are. College, University, whatever Level.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,854
    Thanks
    321
    Awards
    1
    The previously posted solution seems unnecessarily complicated. Let's try:

    2x+1 = x \, log A

    2x + x \, log A = -1

    x(2 + log A) = -1

    x = \frac{-1}{2 + log A}

    -Dan

    PS Ticbol, I learned logarithms the same way you did: log by itself should represent log_{10}. Right or wrong many people in the field DO use log to represent ln. I think it's silly since if they mean ln they should just write it. However my personal preferences don't seem to have any impact on professional Math writing. (Yet. )
    Last edited by topsquark; May 22nd 2006 at 04:56 AM. Reason: Addendum
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Nov 2005
    From
    Wethersfield, CT
    Posts
    92
    Hi:


    From 2x+1 = xlogA, xlog(A) - 2x = 1. Factoring gives x[log(A) - 2] = 1. Therefore x = 1/[log(A) - 2].

    Regards,

    Rich B.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631

    Smile

    Quote Originally Posted by topsquark
    The previously posted solution seems unnecessarily complicated. Let's try:

    2x+1 = x \, log A

    2x + x \, log A = -1

    x(2 + log A) = -1

    x = \frac{-1}{2 + log A}

    -Dan

    PS Ticbol, I learned logarithms the same way you did: log by itself should represent log_{10}. Right or wrong many people in the field DO use log to represent ln. I think it's silly since if they mean ln they should just write it. However my personal preferences don't seem to have any impact on professional Math writing. (Yet. )
    I do not know about "Professional Math writing", but I believe log is log to the base 10, and ln is log to the base e.

    My old Calculus textbook calls log as log to the base e. I just do not believe that book on that. I do not have to conform to everything that book, or any book, says. I always believe what I want to believe.
    Believe me, I am stubborn. I let nobody or whatbody (:-)) dictates me what to believe.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,854
    Thanks
    321
    Awards
    1
    Quote Originally Posted by Rich B.
    Hi:


    From 2x+1 = xlogA, xlog(A) - 2x = 1. Factoring gives x[log(A) - 2] = 1. Therefore x = 1/[log(A) - 2].

    Regards,

    Rich B.
    It was too cold last night. My Math skills are frozen! (Apologies!)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ticbol
    log is log to the base ten
    ln is natural log, or log to the base e.
    I do not assume. That's what they are. College, University, whatever Level.
    We may not like it but the situation with logs is as bad as it is with the
    normalisation of the Fourier Transform. There are a number of conventions
    in use in different fields, ignoring it won't make it go away.

    This link is to the Wikipedia article which explains the ambiguous usage of log

    RonL
    Last edited by CaptainBlack; May 22nd 2006 at 07:43 AM.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by CaptainBlack
    We may not like it but the situation with logs is as bad as it is with the
    normalisation of the Fourier Transform. There are a number of conventions
    in use in different fields, ignoring it won't make it go away.

    This link is to the Wikipedia article which explains the ambiguous usage of log

    RonL
    Well, let the wikipedia people say that. Like I said, my Calculus book, calls log as log to the base e also. I do not believe those. I do not ignore those either. I just look at the context of what is written and if I see that the log there is supposed to be ln, then I see that log as ln. Just so I can follow what is being said.
    It is no big deal to me. I am used to it.
    Just because those guys use log to mean ln to stay with the Math society does not mean I join them. No. To or for me, log is to the base 10 and ln is to the base e.

    In my everyday calculator, log is to the base 10 and ln is to the base e. It is a Texas Instrument model.
    I also have a TI-86, which I do not know how to use, which I am lazy enough to learn how to use, where log is to the base 10 and ln is to the base e.
    Wikipedia is more believable or credible than a TI calculator to students of Math? Crazy comparison, I know, but that is the point. Mathematicians do not need to appear "higher" than us students of Math that they have to confuse us with log for ln.

    I do not allow them Mathematicians to fool me, anyway. Nope.

    Log is to the base 10. Ln is to the base e. Let them wikipedia authors and them Mathematicians cry.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] logarithm equation!! need help solving...
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: December 22nd 2010, 09:43 PM
  2. solving logarithm
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 2nd 2010, 04:00 AM
  3. Help with solving this logarithm
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 2nd 2010, 09:08 PM
  4. Solving for x in a logarithm
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 21st 2009, 06:53 AM
  5. Need help solving this logarithm
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 17th 2008, 05:34 AM

Search Tags


/mathhelpforum @mathhelpforum