Results 1 to 5 of 5

Math Help - 3^x=12x-9

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    1

    3^x=12x-9

    How would one go about solving this algebraically?
    I understand that I can graph it and find the points of intersection, in which case the answers are 1 and 3.

    Can anyone provide a step by step solution to this problem algebraically?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,648
    Thanks
    1596
    Awards
    1

    Re: 3^x=12x-9

    Quote Originally Posted by physicsdreams View Post
    How would one go about solving this algebraically?
    I understand that I can graph it and find the points of intersection, in which case the answers are 1 and 3. Can anyone provide a step by step solution to this problem algebraically?
    One does not solve this type of equation using algebraically.
    You need to understand the Lambert W Function.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: 3^x=12x-9

    "By inspection" 3^1= 3= 12(1)- 9 so one solution is x= 1.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,648
    Thanks
    1596
    Awards
    1

    Re: 3^x=12x-9

    Quote Originally Posted by HallsofIvy View Post
    "By inspection" 3^1= 3= 12(1)- 9 so one solution is x= 1.
    One question: Does inspection qualify as an algebraic solution?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: 3^x=12x-9

    I would say it does! It does suffer from the weakness of not telling whether that is the only solution or not!
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum