Question

6) Determine o valos dos logaritmos:

a)
$log_{2}256$
b)
$log_{ \binom{1 }{3} }81$
c)
$log(1000)$
​

Answer 1

a) 8

b) -4

c) 3

$\Large{\sf{\Huge ————————————————}}$

Algumas coisas importantes:

• Quando não houver base, o valor será 10
• Use $\large\gray{\sf{ _{a}(a^{x}) = x\:log_{a}(a) }}$ e $\large\gray{\sf{ _{a^{y}}(a^{x}) =\frac{x}{y} }}$

$\sf\large \red{ log_{2}(256) } \\ \large \sf \green{log_{2}(2^{8}) }\\ \large \sf \blue{ 8\: log_{2}(2) }\\ \large \sf \pink{8 } \purple{ \times} \orange{1 } \\ \Huge\boxed{\large \sf \red{ 8 } }$

$\:$

$\sf \large \red{ log_{\frac{1}{3}}(81) }\\ \large \sf \green{ log_{3^{-1}} (3^{4}) }\\ \large \sf \blue{\frac{4}{-1}log_{3}(3) }\\ \large \sf \pink{ -4 } \purple{ \times } \orange{ 1 }\\ \Huge\boxed{\large \sf \red{ -4 }}$

$\:$

$\sf \large \red{ log(1000 ) } \\ \large \sf \green{ log_{10}(1000) }\\ \large \sf \blue{ log_{10}(10^{3} ) } \\ \large \sf \pink{ 3\:log_{10}(10 ) } \\ \large \sf \purple{ 3 } \orange{ \times } \red{ 1 }\\ \Huge\boxed{\large \sf \green{ 3 }}$