Results 1 to 3 of 3

Math Help - General Statement

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    8

    Exclamation General Statement

    Let Logax = c and Logbx = d

    I need to find the general statement that expresses Logabx in the form of c and d
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,663
    Thanks
    603
    Hello, Bzaher!

    Let: . \begin{array}{ccc}\log_ax \:=\:c \\ \log_bx \:=\:d \end{array}

    Find the \log_{ab}x in terms of c and d.

    \begin{array}{cccccc}\log_ax \:=\:c & \Rightarrow& a^c \:=\:x & \Rightarrow & a \:=\:x^{\frac{1}{c}} & [1] \\<br />
\log_bx\:=\:d & \Rightarrow & b^d \:=\:x & \Rightarrow & b \:=\:x^{\frac{1}{d}} & [2] \end{array}


    Multiply [1] and [2]: . ab \:=\:x^{\frac{1}{c}}\cdot x^{\frac{1}{d}} \;=\;x^{\frac{1}{c} + \frac{1}{d}} \quad\Rightarrow\quad ab \;=\;x^{\frac{c+d}{cd}}

    Therefore: . ab^{\frac{cd}{c+d}} \;=\;x \quad\Rightarrow\quad \log_{ab}x \;=\;\frac{cd}{c+d}


    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    8
    Thank you so much for the answer, but why is it x to the power of 1/c and 1/d
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Statement neg
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: August 28th 2011, 07:02 AM
  2. Finding the General Statement
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 11th 2011, 11:45 AM
  3. Replies: 4
    Last Post: January 4th 2010, 07:09 PM
  4. logic statement
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: September 16th 2008, 05:36 AM
  5. Disprove a statement
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 16th 2007, 08:30 AM

Search Tags


/mathhelpforum @mathhelpforum