Calcule o valor de K = log 3 (enbaixo pequeno) 27 - log 1/4 (embaixo pequeno) 128 + log 1000
Dado log 2 = 0,301 e log 3 = 0,477 e log 7 = 0,804 calcule
log 12
log 42
log 49/4
1)
K = log[3] 27 - log[1/4] 128 + log 1000
K = log[3] 3³ - log[1/4] 2⁷ + log 10³
K =3* log 3log 3 - 7*log 2/log (1/4) +3* log 10³
K =3 - 7*log 2/(-2log 2) +3
K =3 - 7/(-2) +3 =6+7/2=19/2
2)
a)
log 12= log 4*3=log 4 +log 3
=log 2² + log 3 = 2log2+log 3
b)
log 42= log 7 * 6=log 7 +log 6
=log 7 + log 2*3
=log 7 + log 2+log 3
c)
log 49/4=log 49 - log 4
=log 7² - log 2²
=2log7-2log 2
Propriedades dos Logarítimos
log[a] b = x => b=a^x ->[a] é a base
log(a) b=log b/log a ==>mudança de base
log a/b=log a-log b
log a*b=log a+log b
b*log a= log a^b
(1/b)*log a= log a^(1/b)
log 10 =1, pois 10^1=10
log 5= log10/2=log 10 - log 2=1-log 2
log a = - colog a
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Comments
1)
K = log[3] 27 - log[1/4] 128 + log 1000
K = log[3] 3³ - log[1/4] 2⁷ + log 10³
K =3* log 3log 3 - 7*log 2/log (1/4) +3* log 10³
K =3 - 7*log 2/(-2log 2) +3
K =3 - 7/(-2) +3 =6+7/2=19/2
2)
a)
log 12= log 4*3=log 4 +log 3
=log 2² + log 3 = 2log2+log 3
b)
log 42= log 7 * 6=log 7 +log 6
=log 7 + log 2*3
=log 7 + log 2+log 3
c)
log 49/4=log 49 - log 4
=log 7² - log 2²
=2log7-2log 2
Propriedades dos Logarítimos
log[a] b = x => b=a^x ->[a] é a base
log(a) b=log b/log a ==>mudança de base
log a/b=log a-log b
log a*b=log a+log b
b*log a= log a^b
(1/b)*log a= log a^(1/b)
log 10 =1, pois 10^1=10
log 5= log10/2=log 10 - log 2=1-log 2
log a = - colog a
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