Results 1 to 4 of 4

Thread: Exponential

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    51

    Exponential

    Gosh, i know the basic of exponentials, but when it contains some complex algebra stuff in there, i go blank.

    I know to subtract the 10, but thats it...

    $\displaystyle e^2x-7e^x + 10 = 0$ (its e to the 2x power)


    Thanks a bunch!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member woof's Avatar
    Joined
    Apr 2009
    Posts
    31
    Solve for x: $\displaystyle e^{2x}-7e^x + 10 = 0$ (you need to surround your exponent with braces if it has more than one item in it).


    Let $\displaystyle u=e^x$, and then you have the quadratic $\displaystyle u^{2}-7u+ 10 = (u-2)(u-5)=0$, and therefore

    u=5 or u=2

    $\displaystyle e^x=5$ or $\displaystyle e^x=2$

    Then x=ln 5 or x=ln 2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    51
    Is there another way without using $\displaystyle variable = e^x$?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,767
    Thanks
    3027
    Do you mean "is there a harder way"? Of course, you don't have to replace $\displaystyle e^x$, that's just the simplest thing to do. You could recognise that $\displaystyle e^{2x}- 7e^x+ 10= (e^x- 2)(e^x- 5)= 0$ and then arguing that either $\displaystyle e^x- 2= 0$ or $\displaystyle e^x- 5= 0$.

    And how do I recognise that factoring? Well, I recognize $\displaystyle e^{2x}- 7e^x+ 10$ as a "quadratic in $\displaystyle e^x$" which is essentially replacing $\displaystyle e^x$, at least in my head, by a single variable.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Jun 9th 2011, 09:54 AM
  2. exponential?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Jan 22nd 2010, 11:15 AM
  3. exponential
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Nov 1st 2009, 10:48 AM
  4. exponential
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Aug 17th 2007, 01:31 AM
  5. exponential
    Posted in the Algebra Forum
    Replies: 10
    Last Post: May 1st 2007, 11:02 AM

Search Tags


/mathhelpforum @mathhelpforum