Question

Usando a definição, calcule estes logaritmos:
a) log8 2048=
b) log 100000000=
c)log5 3125=
d)log1/4 512=

Answer 1

a) log₈ 2048

= log 2048/log 8

=log2¹¹/log 2³

=11*log 2/3*log 2

=11/2 =5,5

b)

log 100000000

= log 10⁸=8*log 10 =8*1=8

c)

log₅3125

=  log₅ 5⁵ =5*log₅ 5 =5*1=5

d)

log(1/4)  512

= log 512/log (1/4)

=log 2⁹/ log (1/2²)

=log 2⁹ /log 2⁻²

=9 * log 2/ (-2)*log 2 =9/(-2)=-9/2=-4,5

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Propriedades

log[a] b = log b/log a    ...[a] é a base

log a^b =b* log a

log[b] b   ..para b>0  ==>>log[b] b=1

log (1/a^b) = log a^(-b) = -b * log a