Results 1 to 2 of 2

Thread: Solving the unknown base of exponents

  1. #1
    Newbie
    Joined
    Jan 2008
    From
    Australia
    Posts
    11

    Solving the unknown base of exponents

    So i realised that exponents are the same thing as indices which I put down to the different countries that we all come from.

    Anyway - I have this question which i didn't really know how to approach:

    solve for 'x':

    x^3/2 = 8^1/2 * 9^1/3 / 6^4/3


    I did some working and got:
    x^3/2 = 2^3/4 * 3^-1/4

    I'm not sure if my working was right, but even so, I don't know how to proceed with this question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, Ogsta101!

    Solve for $\displaystyle x\!:\;\;x^{\frac{3}{2}} \;=\;\frac{8^{\frac{1}{2}}\cdot9^{\frac{1}{3}}}{6^ {\frac{4}{3}}} $
    Note that all the bases have factors of 2 or 3.

    We have: .$\displaystyle x^{\frac{3}{2}} \;=\;\frac{\left(2^3\right)^{\frac{1}{2}}\cdot\lef t(3^2\right)^{\frac{1}{3}}} {(2\cdot3)^{\frac{4}{3}}} \;=\;\frac{2^{\frac{3}{2}}\cdot3^{\frac{2}{3}}}{2^ {\frac{4}{3}}\cdot3^{\frac{4}{3}}}\quad\Rightarrow \quad x^{\frac{3}{2}} \;=\;\frac{2^{\frac{1}{6}}}{3^{\frac{2}{3}}}$

    Raise both sides to the power $\displaystyle \frac{2}{3}\!:\;\;\left(x^{\frac{3}{2}}\right)^{\f rac{2}{3}} \;=\;\left(\frac{2^{\frac{1}{6}}}{3^{\frac{2}{3}}} \right)^{\frac{2}{3}}$

    Therefore: .$\displaystyle \boxed{x\;=\;\frac{2^{\frac{1}{9}}}{3^{\frac{4}{9} }} } $

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding unknown base from equation
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Jan 31st 2011, 09:36 PM
  2. Subtracting exponents with the same base
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Nov 22nd 2010, 10:58 PM
  3. Solving for unknown
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jun 9th 2010, 08:02 AM
  4. base and exponents!!!! HELP ME!!!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Jan 3rd 2009, 12:35 PM
  5. logs and exponents of natural base
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Jan 27th 2007, 06:23 AM

Search tags for this page

Click on a term to search for related topics.

Search Tags


/mathhelpforum @mathhelpforum