Question

2- Qual e o valor de:

Answer 1

Explicação passo-a-passo:

a)

$\sf log_{3}~\dfrac{81}{27}$

$\sf =log_{3}~81-log_{3}~27$

$\sf =log_{3}~3^4-log_{3}~3^3$

$\sf =4\cdot log_{3}~3-3\cdot log_{3}~3$

$\sf =4\cdot1-3\cdot1$

$\sf =4-3$

$\sf =\red{1}$

b)

$\sf log_{4}~(1024\cdot256)$

$\sf =log_{4}~1024+log_{4}~256$

$\sf =log_{4}~4^5+log_{4}~4^4$

$\sf =5\cdot log_{4}~+4\cdot log_{4}~4$

$\sf =5\cdot1+4\cdot1$

$\sf =5+4$

$\sf =\red{9}$

c)

$\sf log_{10}~10^{-2}$

$\sf =(-2)\cdot log_{10}~10$

$\sf =(-2)\cdot1$

$\sf =\red{-2}$

Answer 2

Oie, Td Bom?!

a)

$= log_{3}( \frac{81}{27} )$

$= log_{3}(3)$

$= 1$

b)

$= log_{4}(1024 \: . \: 256)$

$= log_{4}(262144)$

$= log_{4}(4 {}^{9} )$

$=9 log_{4}(4)$

$= 9 \: . \: 1$

$= 9$

c)

$= log_{10}(10 {}^{ - 2} )$

$= - 2 log_{10}(10)$

$= - 2 \: . \: 1$

$= - 2$

Att. Makaveli1996