Results 1 to 3 of 3

Math Help - Exponential and Logarithmic Functions

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    9

    Exponential and Logarithmic Functions

    Kinda lost on this problem.



    Would appreciate some help. Does this have to do with log properties?

    -Auburn
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,796
    Thanks
    1576
    No need for logarithms, just convert everything to the same base.

    \displaystyle \frac{25^{3x^2}}{5^{7x}} = \frac{1}{25}

    \displaystyle \frac{(5^2)^{3x^2}}{5^{7x}} = \frac{1}{5^2}

    \displaystyle \frac{5^{6x^2}}{5^{7x}} = 5^{-2}

    \displaystyle 5^{6x^2 - 7x} = 5^{-2}

    \displaystyle 6x^2 - 7x = -2

    \displaystyle 6x^2 - 7x + 2 = 0

    \displaystyle 6x^2 - 3x - 4x + 2 = 0

    \displaystyle 3x(2x - 1) - 2(2x - 1) = 0

    \displaystyle (2x-1)(3x-2) = 0

    \displaystyle 2x-1 = 0 or \displaystyle 3x-2 = 0

    \displaystyle x = \frac{1}{2} or \displaystyle x = \frac{2}{3}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    9
    Right, I see now. Since it's the same base the exponents must be equal. Thank you kindly!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential and Logarithmic Functions
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 23rd 2010, 03:04 PM
  2. exponential & logarithmic functions
    Posted in the Calculators Forum
    Replies: 4
    Last Post: November 27th 2009, 07:59 PM
  3. Exponential and logarithmic Functions help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 6th 2009, 05:16 PM
  4. Logarithmic and Exponential Functions?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 23rd 2008, 03:00 PM
  5. Exponential and Logarithmic Functions help!!!
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 24th 2007, 09:35 PM

Search Tags


/mathhelpforum @mathhelpforum