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what is solution x, 2^x=2^(-x)?
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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.
Posted by sciencesolve on December 31, 2011 at 11:45 PM (Answer #1)
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