Question

EQUAÇÃO EXPONENCIAL

Answer 1

Resposta:

$a)\\ 2^x=8\\ \\ \not2^x=\not2^3\\ \\ x=3$

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$b)\\ 25^t=\sqrt[3]{5} \\ \\ (5^2)^t=5^{1\over3}\\ \\ \not5^{2t}=\not5^{1\over3}\\ \\ 2t={1\over3}\\ \\ 6t=1\\ \\ t={1\over6}$

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$c)\\ 9^x={1\over27}\\ \\ (3^2)^x={1\over3^3}\\ \\ \not3^{2x}=\not3^{-3}\\ \\ 2x=-3\\ \\ x=-{3\over2}$

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$d)\\ ({2\over7})^{x^2-3}=({49\over4})^x\\ \\ ({2\over7})^{x^2-3}=({4\over49})^{-x}\\ \\ ({2\over7})^{x^2-3}=[({2\over7})^2]^{-x}\\ \\ x^2-3=-2x\\ \\ x^2+2x-3=0$

equação do 2º grau

Calcular pela fatoração

( x + 3 )( x - 1)=0

x = -3  

x = 1

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$e)\\ ({2\over3})^x.({4\over9})^{-x}={3^3\over2^3}\\ \\ ({2\over3})^x.({2\over3})^{-2x}=({2\over3})^{-3}\\ \\ ({2\over3})^{x-2x}=({2\over3})^{-3}\\ \\ x-2x=-3\\ \\ -x=-3\\ \\ x=3$

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$f)\\ 8^x.2^x^{2} }=1\\ \\ 2^{3x}.2^x^{2} =2^0\\ \\ 2^{3x+x^2}=2^0\\ \\ 3x+x^2=0\\ \\ x^2+3x=0\\ \\ \\ x(x+3)=0\\ \\ x=-3\\ x=0$

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$h)\\ {5^{{1\over2}(x+1)}\over5^{2x}}=5^3\\ \\ 5^{x+1\over2}=5^3.5^{2x}\\ \\ 5^{x+1\over2}=5^{3+2x}\\ \\{x+1\over2}=3+2x\\ \\ x+1=6+4x\\ \\ 4x-x=1-6\\ \\ 3x=-5\\ \\ x=-{5\over3}$

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$i)\\ (2.3)^x=\sqrt[5]{6^2} \\ \\6^x=6^{2\over5}\\ \\ x={2\over5}$

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Pulei d → numeração ficou trocada

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$d)\\({3\over5})^{x^2}=[({3^3\over5^3})]^x\\ \\ ({3\over5})^x^2}=({3\over5})^{3x}\\ \\ x^2=3x\\ \\ x^2-3x=0\\ \\ x(x-3)=0\\ \\ x=0\\ x=3$