Question

sendo log2 = 0,30 e log3= 0,47 , calcule

a) log 8=

b) log 24=

c) log 20=

d) log 300=


me ajuda fazendo favor e trabalho anual
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Answer 1

Resposta:

$a) 0,90\qquad b)1,37\qquad c) 1,30\qquad d) 2,47$

Explicação passo-a-passo:

Log 2= 0,30                       Log 3 = 0,47

$a) Log 8 =\qquad 8= (2)^3\\\\Log 2^3= \\\\3.Log2 = \\\\3.(0,30) = 0,90\\\\\boxed{Log 8= 0,90} \\\\\\b) Log24=\qquad 24= 3.(2)^3\\\\Log3. 2^3= \\\\log 3 + Log2^3=\\\\Log3 + 3.Log2\\\\(0,47) + 3.(0,30) = 1,37\\\\\boxed{Log24=1,37}$

$c)Log20 =\qquad 20=2.10\\\\Log(2.10)=\\\\Log2+Log10=\\\\(0,30)+1=1,30\\\\\boxed{Log20=1,30}\\\\\\ Log300=\qquad 300=3.100\\\\Log(3.100)= \\\\Log3+Log100=\\\\0,47+ 2=2,47\\\\\boxed{Log300=2,47}$