sabendo que log2=0,3010 log3=0,4771 log5=0,699 log7=0,8450 determine
Soluções para a tarefa
Resposta:
a) 2,5562 b) 0,8751 c) 0,67725 d) 3,1636 e) 1,08355 f) 1,991 g) 0,011
Explicação passo-a-passo:
a) Log 180 -> log (2³.3².5) -> log 2³ + log 3² + log 5 -> 3.log 2 + 2.log 3 + log 5 -> 3.0,3010 + 2.0,4771 + 0,699 ->
0,903 + 0,9542 + 0,699 = 2,566
b) Log 45/6 -> log 45 - log 6 -> log (3².5) - log (2.3) -> 2.log 3 + log 5 - log 2 - log 3 -> 2.0,4771 + 0,699 - 0,3010 - 0,4771 -> 0,9542 + 0,699 - 0,3010 - 0,4771 = 0,8751
c) Log (√ quarta) 512 -> log 512¼ -> log (2⁹)¼ -> log 2⁹/⁴ ->
9/4.0,3010 = 0,67725
d) Log 1458 -> log (2.3⁶) -> Log 2 + Log 3⁶ -> 0,3010 + 6.log 3 -> 0,3010 + 6.0,4771 -> 0,3010 + 2,8626 = 3,1636
e) Log √147 -> log 147½ -> log (3.7²)½ -> log 3½ + log 7¹ ->
1/2.log 3 + 0,8450 -> 0,5.0,4771 + 0,8450 -> 0,23853 + 0,8450 = 1,08355
f) Log 98 -> log (2.7²) -> log 2 + 2.log 7 -> 0,3010 + 2.0,8450 -> 0,3010 + 1,69 = 1,991
g) Log 49/59 -> log 49 - log 50 -> log 7² - log (2.25²) -> 2.log 7 - log 2 - 2.log 5 -> 2.0,8450 - 0,3010 - 2.0,699 -> 1,69 - 0,3010 - 1,98 -> 1,69 - 1,679 = 0,011
Observação -> . = multiplicação