Results 1 to 4 of 4

Math Help - Log equations

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    21

    Log equations

    Solve for x

    2e^(3x) = 4e^(5x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,719
    Thanks
    634
    Hello, cm3pyro!

    Solve for x\!:\;\;2e^{3x} \:= \:4e^{5x}

    We have: . 4e^{5x} \:=\:2e^{3x}

    Divide by 4e^{3x}\!:\;\;e^{2x} \:=\:\frac{1}{2}

    Take logs: . \ln(e^{2x}) \:=\:\ln\left(\frac{1}{2}\right)

    Then: . 2x\!\cdot\!\ln(e) \:=\:\ln(2^{-1}) \quad\Rightarrow\quad 2x\cdot1 \:=\:-\ln(2)

    Therefore: . x \;=\;-\frac{1}{2}\ln(2)

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2008
    Posts
    21
    EDIT: I got it, thanks!

    I dont understand what you did here.

    Divide by 4e^(3x): e^(2x) = 1/2
    Last edited by cm3pyro; September 17th 2008 at 09:27 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,719
    Thanks
    634
    Hello again, cm3pyro!

    I dont understand what you did here.

    Divide by 4e^{3x}\!:\;\;e^{2x} \:= \:\frac{1}{2}
    Write it out!


    We had: . 4e^{5x} \;=\;2e^{3x}

    Divide by 4e^{3x}\!:\;\;\frac{4e^{5x}}{4e^{3x}} \;=\;\frac{2e^{3x}}{4e^{3x}}

    . . and that reduces to: . e^{2x} \:=\:\frac{1}{2}\quad\hdots\;\text{ Get it?}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equi Potential Equations or Euler Type Equations
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: April 2nd 2010, 02:58 AM
  2. Replies: 3
    Last Post: February 27th 2009, 07:05 PM
  3. Replies: 3
    Last Post: December 2nd 2008, 10:54 AM
  4. Replies: 1
    Last Post: September 1st 2007, 06:35 AM
  5. Replies: 1
    Last Post: July 29th 2007, 02:37 PM

Search Tags


/mathhelpforum @mathhelpforum