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Index laws

  1. Mar 25, 2013 #1
    1. The problem statement, all variables and given/known data
    I need to get 1/2^x+(2^(x)-1)/2^(x-1) to equal 2-2^-x
    I originally used index laws so 2^-x+2^(1-x)[2^x - 1]
    From there i expanded so that 2^-x + 2 - 2^(1-x) was the result, i'm not sure where to go from here
     
  2. jcsd
  3. Mar 25, 2013 #2
    try bringing the 2^-x on the RHS to the LHS and then proceed. No need to use index laws here till the very end.
     
  4. Mar 25, 2013 #3

    SammyS

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    I assume you want to show that [itex]\displaystyle \ \ 2^{-x}+\frac{2^{x}-1}{2^{x-1}}=2-2^{-x}\ .[/itex]

    Your result looks correct so far.

    Factor a 2 out of [itex]\displaystyle \ \ 2^{1-x}\ .[/itex]
     
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