03 Usando log2 = 0,30, log3 = 0,47 e log5 = 0,69, calcule:

a) log √2 =

b) log 0,5 =

c) log 20 =

d) log 30 + log 90 =

e) log 50 - log 250 =

f) log 32/15 =

Question

03 Usando log2 = 0,30, log3 = 0,47 e log5 = 0,69, calcule:

a) log √2 =

b) log 0,5 =

c) log 20 =

d) log 30 + log 90 =

e) log 50 - log 250 =

f) log 32/15 =

Accepted Answer

Para resolver as questões, usaremos as propriedades dos logaritmos e os valores fornecidos:

1. $ \log 2 = 0,30 $
2. $ \log 3 = 0,47 $
3. $ \log 5 = 0,69 $

**a) $ \log \sqrt{2} $**

$$
\log \sqrt{2} = \log 2^{1/2} = \frac{1}{2} \log 2 = \frac{1}{2} \times 0,30 = 0,15
$$

**b) $ \log 0,5 $**

$$
\log 0,5 = \log \left(\frac{1}{2}\right) = -\log 2 = -0,30
$$

**c) $ \log 20 $**

$$
\log 20 = \log (2 \times 10) = \log 2 + \log 10 = 0,30 + 1 = 1,30
$$

**d) $ \log 30 + \log 90 $**

$$
\log 30 = \log (3 \times 10) = \log 3 + \log 10 = 0,47 + 1 = 1,47
$$
$$
\log 90 = \log (9 \times 10) = \log (3^2 \times 10) = 2\log 3 + \log 10 = 2 \times 0,47 + 1 = 0,94 + 1 = 1,94
$$
$$
\log 30 + \log 90 = 1,47 + 1,94 = 3,41
$$

**e) $ \log 50 - \log 250 $**

$$
\log 50 = \log (5 \times 10) = \log 5 + \log 10 = 0,69 + 1 = 1,69
$$
$$
\log 250 = \log (25 \times 10) = \log (5^2 \times 10) = 2\log 5 + \log 10 = 2 \times 0,69 + 1 = 1,38 + 1 = 2,38
$$
$$
\log 50 - \log 250 = 1,69 - 2,38 = -0,69
$$

**f) $ \log \frac{32}{15} $**

$$
\log \frac{32}{15} = \log 32 - \log 15
$$
$$
\log 32 = \log (2^5) = 5 \log 2 = 5 \times 0,30 = 1,50
$$
$$
\log 15 = \log (3 \times 5) = \log 3 + \log 5 = 0,47 + 0,69 = 1,16
$$
$$
\log \frac{32}{15} = 1,50 - 1,16 = 0,34
$$

03 Usando log2 = 0,30, log3 = 0,47 e log5 = 0,69, calcule: ...

03 Usando log2 = 0,30, log3 = 0,47 e log5 = 0,69, calcule:

a) log √2 =

b) log 0,5 =

c) log 20 =

d) log 30 + log 90 =

e) log 50 - log 250 =

f) log 32/15 =

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