Question

a) Log'2  16

b) Log'4 16 

c) Log'3 81

d) Log'5 125

e) Log 100.000

f) Log'8 64

Answer 1

E aí Raphael,

use a propriedade da potência e a decorrente da definição:

$logb^k~\to~k\cdot logb\\log_kk=1$

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$log_416=log_44^2\\ log_416=2\cdot log_44\\ log_416=2\cdot1\\\\ \boxed{\boxed{log_416=2}}\\.$

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$log_381=log_33^4\\ log_381=4\cdot log_33\\ log_381=4\cdot1\\\\ \boxed{\boxed{log_381=4}}\\.$

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$log_5125=log_55^3\\ log_5125=3\cdot log_55\\ log_5125=3\cdot1\\\\ \boxed{\boxed{log_5125=3}}\\.$

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$log100.000=log_{10}10^5~~.\\ log100.000=5\cdot log_{10}10\\ log100.000=5\cdot1\\\\ \boxed{\boxed{log100.000=5}}\\.$

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$log_864=log_88^2\\ log_864=2\cdot log_88~~~~~~~.\\ log_864=2\cdot1\\\\ \boxed{\boxed{log_864=2}}\\.$

Ótimos estudos mano =))