Results 1 to 2 of 2

Math Help - Exponential Inequalities

  1. #1
    scy
    scy is offline
    Newbie
    Joined
    Oct 2008
    Posts
    1

    Exponential Inequalities

    Hi,

    Could anyone help me solve the following inequalities algebraically?

    2^x-3<x+1
    (x+1)(x-2)(2^x)>0

    My teacher mentioned something about Newton's method for solving the first one, but he wouldn't explain it to us. I did some research, but I still don't really understand, other than that I have to estimate a zero of 2^x-x-4>0 and use tangents to find a very close approximation of the actual root. As for the second, I can come up with the answer through reasoning and logic, but I would like to know how to solve it algebraically.

    Thanks in advance! =]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by scy View Post
    Hi,

    Could anyone help me solve the following inequalities algebraically?

    ...
    (x+1)(x-2)(2^x)>0

    ..., but I would like to know how to solve it algebraically.
    The LHS of the inequality is a positive product.

    Since 2^x>0 for all x \in \mathbb{R} the sign of the LHS depends on the product (x+1)(x-1).

    A product of 2 factors is positive if the signs of the factors are equal. Thus you get:

    x+1>0\ \wedge\ x-1>0~\vee~x+1<0\ \wedge\ x-1<0

    x>-1\ \wedge\ x>1~\vee~x<-1\ \wedge\ x<1 Therefore

    \boxed{x>1~\vee~x<-1}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: June 9th 2011, 09:54 AM
  2. Inequalities
    Posted in the Algebra Forum
    Replies: 6
    Last Post: August 4th 2009, 02:03 AM
  3. Inequalities
    Posted in the Algebra Forum
    Replies: 3
    Last Post: July 28th 2009, 01:23 AM
  4. Inequalities
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 15th 2009, 11:26 PM
  5. Exponential inequalities
    Posted in the Algebra Forum
    Replies: 7
    Last Post: September 10th 2008, 10:37 PM

Search Tags


/mathhelpforum @mathhelpforum