$$2^{x-2} + 2^{3-x} = 3$$ Please find the value of $x$ and give the solution process.
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2Hint: Multiply both sides by $2^x$. Have a try! – Li Chun Min Jun 20 '17 at 16:06
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$2^{x-2} + 2^{3-x}= 3 $ $ \iff $
$ 2^{x} * \frac{1}{4} + 8*2^{-x} = 3 $ $ \iff (2^{x})^{2} * \frac{1}{4}-3*2^{-x} + 8 = 0 $ we put $2^{x}=y$ we have, $ \frac{1}{4}y²-3y+8=0 \iff y=4 $ or $ y=8 $ now you can find easily that $ x=2 $ and $ x=3 $
ThePirateKing
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HINT:
$$3=\dfrac y{2^2}+\dfrac{2^3}y$$ where $2^x=y$
Now multiply both sides by $y(\ne0)$ for finite $x$
lab bhattacharjee
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See also : https://math.stackexchange.com/questions/384090/find-all-real-numbers-x-for-which-frac8x27x12x18x-frac76 – lab bhattacharjee Jun 20 '17 at 16:07