3) Dados log2 = 0,30, log3 = 0,48 e log5 = 0,70, calcule:

a) log20
b) log0,0002
c) log30000
d) log0,3
e) log500
f) log0,0005

Question

3) Dados log2 = 0,30, log3 = 0,48 e log5 = 0,70, calcule:

a) log20
b) log0,0002
c) log30000
d) log0,3
e) log500
f) log0,0005

Accepted Answer

Para resolver esses logaritmos, usaremos as propriedades dos logaritmos:

1. **Produto**: $\log(ab) = \log a + \log b$
2. **Quociente**: $\log\left(\frac{a}{b}\right) = \log a - \log b$
3. **Potência**: $\log(a^b) = b \log a$

Vamos calcular cada um:

a) $\log 20 = \log (4 \times 5) = \log 4 + \log 5$

$$
\log 4 = \log(2^2) = 2 \log 2 = 2 \times 0{,}30 = 0{,}60
$$

$$
\log 20 = \log 4 + \log 5 = 0{,}60 + 0{,}70 = 1{,}30
$$

b) $\log 0{,}0002 = \log \left(\frac{2}{10000}\right) = \log 2 - \log 10000$

$$
\log 10000 = \log(10^4) = 4 \log 10 = 4 \times 1 = 4
$$

$$
\log 0{,}0002 = \log 2 - 4 = 0{,}30 - 4 = -3{,}70
$$

c) $\log 30000 = \log (3 \times 10000) = \log 3 + \log 10000$

$$
\log 30000 = 0{,}48 + 4 = 4{,}48
$$

d) $\log 0{,}3 = \log \left(\frac{3}{10}\right) = \log 3 - \log 10$

$$
\log 0{,}3 = 0{,}48 - 1 = -0{,}52
$$

e) $\log 500 = \log (5 \times 100) = \log 5 + \log 100$

$$
\log 100 = \log(10^2) = 2 \log 10 = 2 \times 1 = 2
$$

$$
\log 500 = 0{,}70 + 2 = 2{,}70
$$

f) $\log 0{,}00005 = \log \left(\frac{5}{100000}\right) = \log 5 - \log 100000$

$$
\log 100000 = \log(10^5) = 5 \log 10 = 5
$$

$$
\log 0{,}00005 = 0{,}70 - 5 = -4{,}30
$$

Respostas:

a) $\log 20 = 1{,}30$

b) $\log 0{,}0002 = -3{,}70$

c) $\log 30000 = 4{,}48$

d) $\log 0{,}3 = -0{,}52$

e) $\log 500 = 2{,}70$

f) $\log 0{,}00005 = -4{,}30$

3) Dados log2 = 0,30, log3 = 0,48 e log5 = 0,70, calcule: a...

Dados log2 = 0,30, log3 = 0,48 e log5 = 0,70, calcule:

a) log20 b) log0,0002 c) log30000 d) log0,3 e) log500 f) log0,0005

Ask a question and receive an answer instantly

3) Dados log2 = 0,30, log3 = 0,48 e log5 = 0,70, calcule: a...

Dados log2 = 0,30, log3 = 0,48 e log5 = 0,70, calcule: a) log20 b) log0,0002 c) log30000 d) log0,3 e) log500 f) log0,0005

Ask a question and receive an answer instantly

Dados log2 = 0,30, log3 = 0,48 e log5 = 0,70, calcule:

a) log20 b) log0,0002 c) log30000 d) log0,3 e) log500 f) log0,0005