Homework Help

what is solution x, 2^x=2^(-x)?

user profile pic

mouhham | Student, Undergraduate | (Level 1) eNoter

Posted December 31, 2011 at 11:37 PM via web

dislike 0 like

what is solution x, 2^x=2^(-x)?

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted December 31, 2011 at 11:45 PM (Answer #1)

dislike 0 like

You need to solve exponential equation `2^x = 2^(-x).`

Use the property `2^(-x) = 1/2^x`  such that:

`2^x = 1/2^x`

Subtracting `1/2^x`  both sides yields:

`2^x - 1/2^x ` = 0

You need to bring the terms to a common denominator such that:

`(2^(2x) - 1)/2^x`  = 0 => `2^(2x)`  - 1 = 0

You need to use the product that results from a difference of squares:

`2^(2x)`  - 1 = (`2^x`  - 1)(`2^x ` + 1) = 0

Cancelling the first factor yields:

`2^x`  - 1= 0 => `2^x`  = 1

You need to remember that any number raised to 0 power yields 1 => x = 0.

`2^x`  + 1 = 0 => `2^x ` = -1

This equation does not hold for any x since `2^x`  > 0.

The solution to this equation is x = 0.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes