Question

expressao logaritma me ajudem pfv​

Answer 1

Resposta:

Leia abaixo

Explicação passo-a-passo:

$\boxed{log_{100}0,001 + log_{1,5}\frac{4}{9} - log_{1,25}0,64}$

$\boxed{\frac{log 0,001}{log 100} + \frac{log \frac{4}{9} }{log1,5} - \frac{log 0,64}{log 1,25} }$

$\boxed{\frac{log 0,001}{log 100} - \frac{log \frac{4}{9} }{log1,5} - \frac{log 0,64}{log 1,25} }$

$\boxed{\frac{log 10^{-3}}{log 100 } + \frac{log \frac{4}{9} }{log \frac{15}{10} } - \frac{log \frac{64}{100} }{log \frac{125}{100} } }$

$\boxed{\frac{log 10^{-3}}{log 10^2 } + \frac{log \frac{2^2}{3^2} }{log \frac{3.5}{10} } - \frac{log \frac{2^6}{10^2} }{log \frac{5^3}{10^2} } }$

$\boxed{\frac{-3log 10}{2 log 10 } + \frac{2log 2 - 2 log 3 }{log 3 + log 5 - log 10 } - \frac{6log 2 - log 100 }{3log 5 - log 100 } }$

$\boxed{-\frac{3}{2} - \frac{0,35218 }{0,17609 } + \frac{0,19382}{0.09691 } }$

$\boxed{-\frac{3}{2} - 2 + 2 }$

$\boxed{\boxed{-\frac{3}{2}}}}$

Answer 2

Explicação passo-a-passo:

Vamos calcular cada log de uma vez

$\log_{100}0,001=x\\ \\ 100^x=0,001\\ \\ (10^2)^x={1\over1000}\\ \\ 10^{2x}={1\over10^3}\\ \\ 10^{2x}=10^{-3}\\ \\ 2x=-3\\ \\ x=-{3\over2}$

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$\log_{1,5}{4\over9}=x\\ \\ (1,5)^x={4\over9}\\ \\({15\over10})^x={4\over9}\\ \\ ({3\over2})^x={2^2\over3^2}\\ \\ ({3\over2})^x=({2\over3})^2\\ \\ ({3\over2})^x=({3\over2})^{-2}\\ \\ x=-2$

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$\log_{1,25}0,64=x\\ \\ (1,25^)^x=0,64\\ \\ ({125\over100})^x={64\over100}\\ \\ simplificando\\ \\ ({5\over4})^x={16\over25}\\ \\ ({5\over4})^x=({4\over5})^2\\ \\ ({5\over4})^x=({5\over4})^{-2}\\ \\ x=-2$

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Calculando

$-{3\over2}+(-2)-(-2)=\\ \\ -{3\over2}-\not2+\not2=\fbox{ -{3\over2} }$