Results 1 to 3 of 3

Math Help - Logs

  1. #1
    Newbie
    Joined
    May 2006
    Posts
    7

    Logs

    Any help please?

    Line 1: y = a^x + 1 , a>2
    Line 2: y = a^(x+1), a>2

    Prove that they intersect when x = loga(1/(a-1))
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by kenj
    Any help please?

    Line 1: y = a^x + 1 , a>2
    Line 2: y = a^(x+1), a>2

    Prove that they intersect when x = loga(1/(a-1))
    The curves:

    y=a^x+1,\ a>2, and
    y=a^{x+1},\ a>2

    intersect when:

    <br />
a^x+1=a^{x+1}<br />

    so:

    <br />
a^x+1=a.a^x<br />

    Rearranging:

    <br />
a^x(a-1)=1<br />
,

    rearranging:

    <br />
a^x=\frac{1}{a-1}<br />

    so taking \logs to base a:

    <br />
x=\log_a(1/(a-1))=-\log_a(a-1)<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2006
    Posts
    7
    Sorry - got it ! It was easy once I realised that a^(x+1) is the same as aa^x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: February 22nd 2011, 06:39 PM
  2. Logs
    Posted in the Algebra Forum
    Replies: 4
    Last Post: April 24th 2010, 08:52 AM
  3. Logs
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: October 10th 2009, 07:08 PM
  4. Dealing with Logs and Natural Logs
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 14th 2008, 07:18 AM
  5. several questions-logs/natural logs
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: November 12th 2007, 09:58 PM

Search Tags


/mathhelpforum @mathhelpforum