Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By JeffM

Math Help - Having trouble understanding a solution(exponential and logarithmic equations)

  1. #1
    Newbie
    Joined
    Mar 2014
    From
    Canada
    Posts
    2

    Having trouble understanding a solution(exponential and logarithmic equations)

    There is this question

    Solve for x in the following exponential an logarithmic equations



    The solution is as follows

    First use Product Rule to get


    Then use Inversion Rules to get


    Thus


    And from there I can get the x values

    While I understand the product rule I am not sure what is happening when using the inverse rule. I am unsure of where the "log" sign goes or where the number 3 comes from. Any sort of advice as to how you get these equations would be very helpful. Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    607
    Thanks
    168

    Re: Having trouble understanding a solution(exponential and logarithmic equations)

    Hi Dan
    The way you solved the equation it looks like it should be
    log_3(x) + log_3 (2x+1) =1

    With the logs being base 3 and the x in the first log not being raised to the power. Is this what you meant?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Feb 2014
    From
    United States
    Posts
    819
    Thanks
    411

    Re: Having trouble understanding a solution(exponential and logarithmic equations)

    Quote Originally Posted by DanSmith View Post
    There is this question

    Solve for x in the following exponential an logarithmic equations



    The solution is as follows

    First use Product Rule to get


    Then use Inversion Rules to get


    Thus


    And from there I can get the x values

    While I understand the product rule I am not sure what is happening when using the inverse rule. I am unsure of where the "log" sign goes or where the number 3 comes from. Any sort of advice as to how you get these equations would be very helpful. Thank you
    The basic rule concerning logs and exponentials is

    $log_a(b) = c \iff a^c = b.$ Everything else follows from that.

    The log function (not sign) and exponential function are inverses. You can go back and forth between them with this simple little conversion. You need to memorize it. It is definitional.

    ASSUMING your problem is $log_3(x) + log_3(2x + 1) = 1$

    THEN $log_3(x) + log_3(2x + 1) = 1 \implies log_3\{x(2x + 1)\} = 1.$ Product Rule.

    SO $log_3(2x^2 + x) = 1.$ Simplification.

    Now apply the basic inversion rule where $a = 3,\ b = 2x^2 + x,\ and\ c = 1.$

    $log_3(2x^2 + x) = 1 \implies 2x^2 + x = 3^1 = 3 \implies 2x^2 + x - 3 = 0 \implies$

    $(2x + 3)(x - 1) = 0 \implies x = -\ \dfrac{3}{2}\ or\ x = 1.$

    One of those answers is wrong. Which one and why?
    Thanks from Shakarri
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential and Logarithmic Equations
    Posted in the Algebra Forum
    Replies: 8
    Last Post: May 18th 2013, 07:18 PM
  2. Exponential and Logarithmic Equations
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 18th 2013, 04:06 PM
  3. Exponential and Logarithmic Equations
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 1st 2010, 09:11 PM
  4. Trouble with exponential equations
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 11th 2008, 07:22 PM
  5. Exponential and Logarithmic Equations
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: June 15th 2006, 01:08 PM

Search Tags


/mathhelpforum @mathhelpforum