Results 1 to 7 of 7

Math Help - Addition/Subtraction of logarithms

  1. #1
    Member
    Joined
    Oct 2009
    From
    Detroit
    Posts
    195
    Thanks
    5

    Addition/Subtraction of logarithms

    2 log x - {2/3} log x + 4 log x = log x{16/3}

    I'm not confused by the logarithm operations. But apparently the fractional exponents. The answer given above is from the book. I thought it should be something like;
     2*{3/2}*4={24/2}=12
    Last edited by bkbowser; December 2nd 2009 at 08:47 AM. Reason: grammar
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2009
    Posts
    277
    Thanks
    2

    logs

    2 log x - \frac{2}{3} log x + 4 log x<br />

    = log x^2 +log x ^ { -\frac {2}{3}} + log x^4<br />

    = log x^2 x ^ { -\frac {2}{3}} x^4<br />

    = log x^ { 2 -\frac {2}{3} + 4 }

    <br />
 = log x^{16/3}<br />

    Alternatively:

    2 log x - \frac{2}{3} log x + 4 log x<br />

    =(2 - \frac{2}{3} + 4) log x<br />


    =\frac{16}{3} log x<br />

    <br />
 = log x^{16/3}<br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,907
    Thanks
    766
    Hello, bkbowser!

    Why are you multiplying and dividing exponents?


    2\log(x) - \tfrac{2}{3}\log(x) + 4\log(x) \:=\:\log \left(\frac{16}{3}\right)

    We have: . \log\left(x^2\right) - \log\left(x^{\frac{2}{3}}\right) +  \log\left(x^4\right) \:=\: \log\left(\frac{16}{3}\right)

    . . . . . . . \log\left(\frac{x^2\cdot x^4}{x^{\frac{2}{3}}}\right) \:=\:\log\left(\frac{16}{3}\right)

    . . . . . . . \log\left(x^{\frac{15}{3}}\right) \:=\:\log\left(\frac{16}{3}\right)

    "Un-log" both sides: . x^{\frac{16}{3}} \:=\:\frac{16}{3}

    Therefore: . x \:=\:\left(\frac{16}{3}\right)^{\frac{3}{16}}


    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2009
    From
    Detroit
    Posts
    195
    Thanks
    5
    I thought you where supposed to multiply what ever came after the log notation when adding and divide when subtracting. The book never said what too do with exponents beyond to just apply them (2 log 2 = log 4). Since the notation is different enough I'm not really sure what too do most of the time. This gets made worse by the fact that the explanations of how to perform an operation don't include any information on why.

    Oh and they where just asking to combine 3 log terms not solve for anything which it seems like you did to get an x = something statement. I was unclear on that.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Nov 2009
    Posts
    277
    Thanks
    2
    This is not a question of "solve for x". The RHS of the original question is not
    <br />
log (16/3)<br />

    Instead, it is:

    <br />
log (x)^{16/3}<br /> <br />
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2009
    From
    Detroit
    Posts
    195
    Thanks
    5
    Quote Originally Posted by qmech View Post
    This is not a question of "solve for x". The RHS of the original question is not
    <br />
log (16/3)<br />

    Instead, it is:

    <br />
log (x)^{16/3}<br /> <br />
    What is "RHS"?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Nov 2009
    Posts
    277
    Thanks
    2

    Standard abbreviations

    RHS = right hand side
    LHS = left hand side
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Addition Subtraction
    Posted in the Algebra Forum
    Replies: 0
    Last Post: August 25th 2010, 06:43 PM
  2. Addition and Subtraction Formulas
    Posted in the Trigonometry Forum
    Replies: 13
    Last Post: March 16th 2010, 06:39 PM
  3. The Addition and subtraction Formulas
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 16th 2010, 06:31 PM
  4. Addition and Subtraction Properties
    Posted in the Geometry Forum
    Replies: 1
    Last Post: September 27th 2007, 07:56 PM
  5. addition-or-subtraction method...
    Posted in the Algebra Forum
    Replies: 6
    Last Post: May 9th 2007, 03:20 PM

Search Tags


/mathhelpforum @mathhelpforum