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Solve the equation

  • #1
utkarshakash
Gold Member
855
13

Homework Statement


[itex]2^{|x+2|}-|2^{x+1}-1|=2^{x+1}+1[/itex]

Homework Equations



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]
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
956
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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