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2014-06-26T13:24:07-03:00

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Olá Ilane,

Use as propriedades da potenciação e transforme os números decimais em fração:

81^{x-2}= \sqrt[4]{27}\\
(3^4)^{x-2}= \sqrt[4]{3^3}\\
3^{4x-8}=3^{ \tfrac{3}{4} }\\\\
\not3^{4x-8}=\not3^{ \tfrac{3}{4} }\\\\
4x-8= \dfrac{3}{4}\\\\
4x= \dfrac{3}{4}+8\\\\
4x= \dfrac{35}{4}\\\\
x= \dfrac{35}{12}\\\\S=\left\{ \dfrac{35}{12}\right\}

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 \sqrt{4^{x+1} }= \sqrt[3]{16}\\\\
4^{ \tfrac{x+1}{2} }= \sqrt[3]{4^2}\\\\
4^{ \tfrac{x+1}{2} }=4^{ \tfrac{2}{3} }\\\\
\not4^{ \tfrac{x+1}{2} }=\not4^{ \tfrac{2}{3} }\\\\
 \dfrac{x+1}{2}= \dfrac{2}{3}\\\\
3(x+1)=2*2\\\\
3x+3=4\\\\
3x=4-3\\\\
3x=1\\\\
x= \dfrac{1}{3}\\\\
S=\left\{ \dfrac{1}{3}\right\}

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 \sqrt{5^x}*25^{x+1}=(0,2)^{1-x}\\\\
5^{ \tfrac{x}{2} }*(5^2)^{x+1}= \left(\dfrac{1}{5}\right)^{1-x}\\\\\\
5^{ \tfrac{x}{2} }*5^{2x+2}=(5^{-1})^{1-x}\\\\
5^{ \tfrac{x}{2}+2x+2 }=5^{x-1}\\\\
\not5^{ \tfrac{x}{2}+2x+2 }=\not5^{x-1}\\\\
 \dfrac{x}{2}+2x+2=x-1\\\\
 \dfrac{x}{2}=x-1-2x-2\\\\
 \dfrac{x}{2}=-x-3\\\\
x=2(-x-3)\\
x=-2x-6\\
x+2x=-6\\
3x=-6\\\\
x= \dfrac{-6}{~3}\\\\
x=-2\\\\
S=\{-2\}

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\left(\dfrac{2}{5}\right)^{x+3}= \left(\dfrac{125}{8}\right)^{x-1}*(0,4)^{2x-3}\\\\
 \left(\dfrac{2}{5}\right)^{x+3}=\left( \dfrac{5^3}{2^3}\right)^{x-1}*\left( \dfrac{2}{5}\right)^{2x-3}\\\\
\left( \dfrac{2}{5}\right)^{x+3}=\left( \dfrac{5}{2}\right)^{3(x-1)}*\left( \dfrac{2}{5}\right) ^{2x-3}\\\\
\left( \dfrac{2}{5}\right)^{x+3}=\left( \dfrac{2}{5}\right)^{-3*(x-1)}*\left( \dfrac{2}{5}\right)^{2x-3}\\\\


\left( \dfrac{2}{5}\right)^{x+3}=\left( \dfrac{2}{5}\right)^{-3x+3}*\left( \dfrac{2}{5}\right)^{2x-3}\\\\
\left( \dfrac{2}{5}\right)^{x+3}=\left( \dfrac{2}{5}\right)^{-3x+3+2x-3}\\\\
\left( \dfrac{2}{5}\right)^{x+3}=\left( \dfrac{2}{5}\right)^{-x}\\\\\\
x+3=-x\\
-x-x=3\\
-2x=3\\\\
x= \dfrac{~~3}{-2}\\\\
x=- \dfrac{3}{2}\\\\
S=\left\{- \dfrac{3}{2}\right\}

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 \sqrt[5]{2^x}* \sqrt[3]{4^x}= \sqrt{8^{-x} }\\\\
2^{ \tfrac{x}{5} }* \sqrt[3]{(2^2)^{x} }= \sqrt{(2^3)^{-x} }\\\\
2^{ \tfrac{x}{5} }*  \sqrt[3]{2 ^{2x}}= \sqrt{2^{-3x} }\\\\
2^{ \tfrac{x}{5} }*2^{ \tfrac{2}{3}x }=2^{-3x}\\\\
\not2^{ \tfrac{x}{5}+ \tfrac{2}{3}x}=\not2^{-3x}\\\\
 \dfrac{x}{5}+ \dfrac{2}{3}x=-3x\\\\\\



 \dfrac{13x}{15}=-3x\\\\
13x=15*(-3x)\\\\
13x=-45x~\to~sem~soluc\~ao

Espero ter ajudado e tenha ótimos estudos =))
3 5 3
pq a letra e não tem solução?
pq a equação não tem coeficientes numéricos, sem a parte variável
http://brainly.com.br/tarefa/738324 vc póde me ajudar com essa ai tbm