Question

*100 PONTOS*
Sendo log 2 = 0,301 e log 3 = 0,477 calcule(resposta completa pfv):
a) log 200
b) log 0,002
c) log 6
d) log 60
e) log 1,5
f) log 81 na base 2

Answer 1

a)

$\log 200 = \\ \\ \log 2 \cdot100 = \\ \\ \log 2 + \log 100 = \\ \\ 0.301 + 2$

b)

$\log 0.002 = \\ \\ \log \frac{2}{1000} = \\ \\ \log 2 - \log 1000 = \\ \\ 0.301 - 3 = - 2.699$

c)

$\log 6 = \\ \\ \log 2 \cdot3 = \\ \\ \log 2 + \log 3 = \\ \\ 0.301 + 0.477 = 0.778$

d)

$\log 60 = \\ \\ \log 2 \cdot3 \cdot10 = \\ \\ \log 2 + \log 3 + \log 10 = \\ \\ 0.301 + 0.477 + 1 = 1.778$

e)

$\log 1.5 = \\ \\ \log \frac{3}{2} = \\ \\ \log 3 - \log 2 = \\ \\ 0.477 - 0.301 = 0.176$

f)

$\log_{2} 81 = \frac{\log 81}{\log 2} \\ \\ \log_{2} 81 = \frac{\log {3}^{3} }{\log 2} \\ \\ \log_{2} 81 = \frac{3\log 3}{\log 2} \\ \\ \log_{2} 81 = \frac{\log 3(0.477)}{0.301} \\ \\ 4.75$