Question

considerando log2 = 0 3010 e log3 = 0 4771 calcule log 96

Answer 1

Explicação passo-a-passo:

a)

24 | 2

12 | 2

6 | 2

3 | 3

1

Logo, 24 = 2^3.3, assim

log 24 = log 2^3.3 = log 2^3 + log 3 = 2.log 2 + log 3 = 2.0,3010 + 0,4771 = 0,6020 + 0,4771 = 1,0791

b)

96 | 2

48 | 2

24 | 2

12 | 2

6 | 2

3 | 3

1

Logo, 96 = 2^5.3, assim

log 96 = log 2^5.3 = log 2^5 + log 3 = 5.log 2 + log 3 = 5.0,3010 + 0,4771 = 1,5050 + 0,4771 = 1,9821

c)

15 | 3

5 | 5

1

Logo, 15 = 3.5, assim

log 15 = log 3.5 = log 3 + log 5 = log 3 + log 10/2 = log 3 + log 10 - log 2 = 0,4771 + 1 - 0,3010 = 0,8751

d)

2000 = 2.10^3, assim

llog 2000 = log 2.10^3 = log 2 + log 10^3 = log 2 +"3.log 10 = 0,3010 - 3.1 = -2,699