Question

calcule o valor de X

A.
${32}^{x} = 1.024$
B.
${x}^{3} = \frac{1}{27}$
C.
$x = ( {2}^{3}) \frac{1}{2}$
D.
$5 ^{ - x} = \frac{1}{125}$​

Answer 1

Explicação passo-a-passo:

$A)\\ \\ 32^x=1.024\\ \\ (2^5)^x=2^{10}\\ \\ 2^{5x}=2^{10}\\ \\ cancela~~base~~2\\ \\ 5x=10\\ x=10\div5\\ \\ x=2$

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$B)\\ x^3={1\over27}\\ \\ x=\sqrt[3]{{1\over27}} \\ \\ x=\sqrt[3]{({1\over3})^3} \\ \\ x={1\over3}$

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$C)\\ x=(2^3)^{1\over2}\\ \\ x=\sqrt{2^3} \\ \\ x=\sqrt{2^2.2} \\ \\ x=2\sqrt{2}$

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$D)\\ 5^{-x}={1\over125}\\ \\ 5^{-x}=5^{-3}\\ \\ -x=-3~~~\times(-1)\\ \\ x=3$