URGEEENTE EQUAÇÃO EXPONENCIAL: raiz de 1/2^3x-2=1/2^-4x*2^-x+4
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Solução!
![\left ( \sqrt{ \dfrac{1}{2} }\right )^{3x-2}= \left ( \dfrac{1}{2} \right )^{-4x}.2^{-x+4} \\\\\\\\
\left ( \left ( \dfrac{1}{2} }\right )^{ \dfrac{1}{2} }\right )^{3x-2}= \left ( \dfrac{1}{2} \right )^{-4x}.2^{-x+4} \\\\\\\
\left ( 2 }\right )^{- \frac{1}{2}.(3x-2) }\right )=( 2^{-1})^{-4x}.2^{-x+4} \\\\\\\
\left ( 2 }\right )^{ \frac{-3x+2}{2} }\right )=( 2)^{3x+4} \\\\\\\\\\\\
Bases~~iguais!\\\\\\\\
\frac{-3x+2}{2}=3x+4\\\\\\\
-3x+2=6x+8\\\\\\
-3x-6x=8-2\\\\\\
-9x=6\\\\\](https://tex.z-dn.net/?f=%5Cleft+%28+%5Csqrt%7B+%5Cdfrac%7B1%7D%7B2%7D+%7D%5Cright+%29%5E%7B3x-2%7D%3D+%5Cleft+%28+%5Cdfrac%7B1%7D%7B2%7D+%5Cright+%29%5E%7B-4x%7D.2%5E%7B-x%2B4%7D+++%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+%5Cleft+%28+%5Cdfrac%7B1%7D%7B2%7D+%7D%5Cright+%29%5E%7B+%5Cdfrac%7B1%7D%7B2%7D+%7D%5Cright+%29%5E%7B3x-2%7D%3D+%5Cleft+%28+%5Cdfrac%7B1%7D%7B2%7D+%5Cright+%29%5E%7B-4x%7D.2%5E%7B-x%2B4%7D+++%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+2+%7D%5Cright+%29%5E%7B-+%5Cfrac%7B1%7D%7B2%7D.%283x-2%29+%7D%5Cright+%29%3D%28+2%5E%7B-1%7D%29%5E%7B-4x%7D.2%5E%7B-x%2B4%7D+++++%5C%5C%5C%5C%5C%5C%5C%0A%5Cleft+%28+2+%7D%5Cright+%29%5E%7B+%5Cfrac%7B-3x%2B2%7D%7B2%7D+%7D%5Cright+%29%3D%28+2%29%5E%7B3x%2B4%7D++++%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0ABases%7E%7Eiguais%21%5C%5C%5C%5C%5C%5C%5C%5C%0A+%5Cfrac%7B-3x%2B2%7D%7B2%7D%3D3x%2B4%5C%5C%5C%5C%5C%5C%5C%0A-3x%2B2%3D6x%2B8%5C%5C%5C%5C%5C%5C%0A-3x-6x%3D8-2%5C%5C%5C%5C%5C%5C%0A-9x%3D6%5C%5C%5C%5C%5C%0A%0A%0A%0A "\left ( \sqrt{ \dfrac{1}{2} }\right )^{3x-2}= \left ( \dfrac{1}{2} \right )^{-4x}.2^{-x+4} \\\\\\\\
\left ( \left ( \dfrac{1}{2} }\right )^{ \dfrac{1}{2} }\right )^{3x-2}= \left ( \dfrac{1}{2} \right )^{-4x}.2^{-x+4} \\\\\\\
\left ( 2 }\right )^{- \frac{1}{2}.(3x-2) }\right )=( 2^{-1})^{-4x}.2^{-x+4} \\\\\\\
\left ( 2 }\right )^{ \frac{-3x+2}{2} }\right )=( 2)^{3x+4} \\\\\\\\\\\\
Bases~~iguais!\\\\\\\\
\frac{-3x+2}{2}=3x+4\\\\\\\
-3x+2=6x+8\\\\\\
-3x-6x=8-2\\\\\\
-9x=6\\\\\")
![x= -\dfrac{6}{9} \\\\\\\
\boxed{x=- \dfrac{2}{3} }](https://tex.z-dn.net/?f=x%3D+-%5Cdfrac%7B6%7D%7B9%7D+%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bx%3D-+%5Cdfrac%7B2%7D%7B3%7D+%7D "x= -\dfrac{6}{9} \\\\\\\
\boxed{x=- \dfrac{2}{3} }")
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Solução!
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