Question

dados log2=0,3 e log 3=0,48 calcule:
com conta se possivel

Answer 1

Resposta:

Explicação passo-a-passo:

a) $log\ 6 \ =log \ (2\cdot 3) = log\ 2 + log  \ 3=0,3+0,48=0,78$

b)

$log \ 1,5 \\= log \ \Big(\frac{15}{10}\Big)\\=log \ 15 - log \ 10 \\= log \Big(\frac{3\cdot 10}{2}\Big) - log 10 \\= \Big[log \ (3\cdot 10) - log \ 2\Big] - log \ 10\\= \Big[log \ 3 + log \ 10 - log \ 2\Big] - log \ 10\\= log \ 3 + log \ 10 - log \ 2\Big - log \ 10\\= log \ 3 - log \ 2\Big  + log \ 10  - log \ 10\\= 0,48 - 0,3\\=0,18$

c)$log \ 96 = log \ \big(2^5\cdot 3\big)= log \ 2^5 + log \ 3 =5 \cdot log \ 2 + log \ 3 =5\cdot0,3+0,48=1,98$

d)

$log\ 600 =log \ (6\cdot 10^2)\\=log \ 6 + log \ 10^2\\=log \ 6 + 2\cdot log \ 10\\=0,78 + 2\cdot 1\\=0,78 + 2\\=2,78$