Question

O valor de E, é:
a)7/3
b)11/3
c)14/3
d)17/3
e)42​

Answer 1

Resposta:

Letra C

Explicação passo-a-passo:

Calcular separado cada log

$\log_{0,6}{81\over625}=x\\ \\ (0,6)^x={81\over625}\\ \\ ({6\over10})^x={3^4\over5^4}\\ \\ ({3\over5})^x=({3\over5})^4\\ \\ x=4$

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$log10000=x\\ \\ 10^x=10^4\\ \\ x=4$

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$\log_{\sqrt{5} }{\sqrt[3]{625} }=x\\ \\ (\sqrt{5} )^x=\sqrt[3]{5^4} \\ \\ (5^{1\over2})^x=5^{4\over3}\\ \\ 5^{x\over2}=5^{4\over3}\\ \\ {x\over2}={4\over3}\\ \\ 3x=8\\ \\ x={8\over3}$

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$8^{1-\log_84}\\ \\ \log_84=x\\ \\ 8^x=4\\ \\ 2^{3x}=2^2\\ \\ 3x=2\\ x={2\over3}\\ \\ logo\\ \\ 8^{1-{2\over3}}=8^{3-2\over3}=8^{1\over3}=(2^3)^{1\over3}=2$

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-Calculando

$E=\not4-\not4+{8\over3}+2\\ \\ E={8+6\over3}\\ \\ \fbox{ E={14\over3} }$