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The Integral Values Of x Satisfying The Equation 2^|x+1| - 2^x = |2^x - 1| + 1 Are?

Sujoy Das

07/02/2018 2 0

Question:

The integral values of x satisfying the equation,

2^|x+1| - 2^x = |2^x - 1| + 1 are:

Answer:

Method 1:

Case 1 : x > -1

Expression reduces to : 2^x - 1 = |2^x - 1|

=> 2^x - 1 >= 0 => x >=0

Case 2 : x< -1

Put 2^x = t in the expression and solve,

t = 1/4 => x = -2

Integral values : {-2} U [0,infinity).

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