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Solve the equation

  1. Nov 3, 2012 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    [itex]2^{|x+2|}-|2^{x+1}-1|=2^{x+1}+1[/itex]
    2. Relevant equations

    3. The attempt at a solution
    I know this is not a direct equation in quadratic but somehow I have to convert it in that form by assuming something to be another variable. I am supposing [itex]2^x=t[/itex]. But that doesn't help me as I cannot eliminate [itex]2^{|x+2|}[/itex]
     
  2. jcsd
  3. Nov 3, 2012 #2

    HallsofIvy

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    Staff Emeritus
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    The first thing I would do it set up "cases" to handle the absolute values. x+ 2 will be positive for x> -2 and [itex]2^{x+ 1}- 1> 0[/itex] for x> -1. So if x< -2, both x+ 2 and [itex]2^{x+1}-1[/itex] are negative. If -2< x< -1, x+ 2 is positive but [itex]2^{x+1}- 1[/itex] is still negative. If x> -1, both x+ 2 and [itex]2^{x+1}- 1[/itex] are positive.

    Also use the fact that [itex]2^{x+ a}= 2^a 2^x[/itex].
     
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