Log de 0,125 na base 2
Soluções para a tarefa
Respondido por
30
Vamos usar alguns artifícios:
obs: log2^0,125 = x, logo, log2^x = 0,125
Assim: log2^x = 125/1000 125/100 = 5/40 = 1/8
log2^x = 1/8
log2^x = 1/2³
log2^x = 2^-3
x = -3
obs: log2^0,125 = x, logo, log2^x = 0,125
Assim: log2^x = 125/1000 125/100 = 5/40 = 1/8
log2^x = 1/8
log2^x = 1/2³
log2^x = 2^-3
x = -3
Respondido por
12
Boa noite!
Solução!
![log_{2}0,125\\\\\\
log_{2} \frac{125}{1000}\\\\\\
log_{2} (\frac{5}{10})^{3}=x \\\\\\
2^{x}= (\frac{10}{5})^{-3} \\\\\\
2^{x}=2^{-3}\\\\\\
x=-3\\\\\\\\\
\boxed{Resposta: log_{2}0,125~~~~x=-3}](https://tex.z-dn.net/?f=log_%7B2%7D0%2C125%5C%5C%5C%5C%5C%5C%0Alog_%7B2%7D+%5Cfrac%7B125%7D%7B1000%7D%5C%5C%5C%5C%5C%5C%0Alog_%7B2%7D+%28%5Cfrac%7B5%7D%7B10%7D%29%5E%7B3%7D%3Dx+%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D+%28%5Cfrac%7B10%7D%7B5%7D%29%5E%7B-3%7D+%5C%5C%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D2%5E%7B-3%7D%5C%5C%5C%5C%5C%5C%0Ax%3D-3%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A+log_%7B2%7D0%2C125%7E%7E%7E%7Ex%3D-3%7D "log_{2}0,125\\\\\\
log_{2} \frac{125}{1000}\\\\\\
log_{2} (\frac{5}{10})^{3}=x \\\\\\
2^{x}= (\frac{10}{5})^{-3} \\\\\\
2^{x}=2^{-3}\\\\\\
x=-3\\\\\\\\\
\boxed{Resposta: log_{2}0,125~~~~x=-3}")
Boa noite!
Bons estudos!
Solução!
Boa noite!
Bons estudos!
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