Results 1 to 3 of 3

Thread: Indices, logarithms question

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    32

    Indices, logarithms question

    hey there
    been stuck on this one for ages. can't really get a grasp on it

    Given: $\displaystyle 3^x = 4^y = 12^z$ , show that $\displaystyle z = \frac{xy}{x+y}$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2010
    From
    in the 4th dimension
    Posts
    154
    Thanks
    15

    Re: Indices, logarithms question

    Quote Originally Posted by walleye View Post
    hey there
    been stuck on this one for ages. can't really get a grasp on it

    Given: $\displaystyle 3^x = 4^y = 12^z$ , show that $\displaystyle z = \frac{xy}{x+y}$
    Here's one way you can do it :
    We know that $\displaystyle 3^x = 4^y = 12^z$
    now taking logarithms, this equation becomes $\displaystyle \implies x\log 3 = y\log 4 = z\log 12$
    we also write:$\displaystyle x\log 3 = y\log 4 = z\log 12 = k$
    now $\displaystyle \log 3=\frac{k}{x}$ and $\displaystyle \log 4=\frac{k}{y}$

    Also,$\displaystyle z\log 12 = k \implies z\log(4.3)=k $
    by applying the log properties:$\displaystyle \implies z\log 4 + z\log 3 = k \implies z(\log 4 +\log 3)=k$
    putting in the values of $\displaystyle \log 4$ and $\displaystyle \log 3$, $\displaystyle \implies$ $\displaystyle zk(\frac{1}{x}+\frac{1}{y})=k$
    $\displaystyle k$ gets cancelled,and simplifying gives us: $\displaystyle z(\frac{x+y}{xy})=1$
    which gives $\displaystyle z=\frac{xy}{x+y}$


    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    863
    Thanks
    220

    Re: Indices, logarithms question

    Indices, logarithms question-10-aug-2013.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [GCSE-O] Logarithms And Indices
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jun 20th 2013, 10:50 PM
  2. Indices and Logarithms Help
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Dec 5th 2008, 06:32 AM
  3. polynomials,indices,logarithms
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Sep 23rd 2008, 05:50 AM
  4. HELP !! indices and logarithms
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Oct 14th 2007, 08:58 AM
  5. HELP !! on Indices and Logarithms
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Oct 14th 2007, 07:10 AM

Search Tags


/mathhelpforum @mathhelpforum