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What is solution in real number of equation (1/2)^x=2^(x-2)?
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You should use negative power property, such that:
`(1/2)^x = 2^(-x)`
Replacing `2^(-x)` for `(1/2)^x` yields:
`2^(-x) = 2^(x-2)`
Equating the corresponding exponents yields:
`-x = x - 2 => -x - x = -2 => -2x = -2 => x = 1`
Sketching the graphs of the functions `y = 2^(-x)` and `y = 2^(x-2)` , you may notice that they intersect at `x = 1` and `y = 1/2.`
Hence, evaluating the solution to the given exponential equation, using the properties of exponents, yields `x = 1.`
Posted by sciencesolve on July 24, 2013 at 2:33 PM (Answer #1)
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