Question

Dados Log 2 = 0.30 e Log 5 = 0,70, calcule:

a) Log 10 =
b) Log 50 =
c) Log 0,005 =
d) Log 32 =

Answer 1

Olá, siga a explicação:

(Dados Log 2 = 0.30 e Log 5 = 0,70, calcule):

A) Logaritmo de 10:

$\huge {\boxed {\sf log(10) = log(2 \centerdot 5 ) = log (2)+ log(5) =1}}$

B) Logaritmo de 50:

$\huge {\boxed {\sf log(50) = log( 2 \centerdot 5 \centerdot 5) = log(2) + log(5) + log(5)}}$

$\huge {\boxed {\sf log(2) + log(5) + log(5) \approx 1,7}}$

C) Logaritmo de 0,005:

$\huge {\boxed {\sf log(0,005) = \sf log \left ( \cfrac{5}{2 \centerdot 5 \centerdot 2 \centerdot 5 \centerdot 2 \centerdot 5 }\right ) }}$

$\large { \boxed { \boxed {\sf \cfrac{log(5)}{log(2) + log(5) + log (2) + log (5)+ log (2) + log(5) } }}}$

$\large {\boxed { \boxed { \boxed {\sf \cfrac{0,70}{0,30 + 0,70+ 0,30 + 0,70 + 0,30 +0,70} \approx -2,3}}}}$

D) Logaritmo de 32:

$\huge {\boxed { \sf log(32) = log(2 \centerdot 2 \centerdot 2 \centerdot 2 \centerdot 2) }}$

$\huge {\boxed {\sf log(2) + log(2) + log(2) + log(2) + log(2) }}$

$\huge {\boxed {\sf 0,30 + 0,30 + 0,30 + 0,30 + 0,30 \approx 1,5}}$

✍️ Att. MatiasHP