Respostas

  • Usuário do Brainly
2013-05-26T15:58:03-03:00

Dado do Problema:

⅓*log15 ( 8 ) + 2*log15 ( 2 ) + log15 ( 5 ) - log15 (9000)

Propriedades Operatórias dos Logarítmos

log15 ( 8^⅓ ) + log15 ( 2² ) + log15 ( 5 ) - log15 (9x10³)
= log15 ( 2 ) + log15 ( 4 ) + log15 ( 5 ) - log15 (9x10³)

Mas = log15 ( 2 ) + log15 ( 4 ) = log15 (8),
logo temos:

= log15 ( 8 ) + log15 ( 5 ) - log15 (9x10³)
= log15 ( 8x5/ 9x10³) 

= log15 ( 40/9x10^³) 
= log15 ( 40/9000 ) 
= log15 ( 4/900 )
Simplificando 4/900 = 1/225

= log15 ( 1/225 ), mas 225 = 15² 

= log15 ( 1/15² ) 
= log15 (15^-² ) 

= -2*log15 (15 ) 
= -2*1
= -2

Resposta:
⅓*log15 ( 8 ) + 2*log15 ( 2 ) + log15 ( 5 ) - log15 (9000) = -2

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