Question

Usando a definição de logaritmos, calcule:?
a) log100000
b) log1/2 32
c) log2/3 8/27
d) log2 0,25
e) log7 7
f) log4 1
g) log1/5 1/5

Answer 1

Olá Mikaelle

a) 10^x = 100000 = 10^5 ⇒ x = 5 

b) log1/2(32) = log2(1/32) ⇒ 2^x = 2^-5 ⇒ x = -5

c) log2/3(8/27) = log2/3(2/3^3) = 3

d) log2(1/4) ⇒ 2^x = 2^-2 ⇒ x = -2 

e) log7(7) = 1

f) log4(1) = 0

g) log1/5(1/5) = 1

Answer 2

a) log100000 = x ==> 10^x = 100000==> 10^x =10^5 ==> x= 5
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b) log1/2 = x ==> 32^x = 1/2==> (2^5)^x = 2^-1 ==> 5x= -1 ==> x = - 1/5
        32
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c) log2/3 = x ==> 2/3^x = 8/27==> 2/3^x = (2/3)³ ==> x= 3
        8/27
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d) log2    = x ==>0,25^x = 2==> (1/4)^x = 2^1 ==>(2^5)^x = 2^-1 ==> 5x= -1 
        0,25

 ==>0,25^x = 2==> (1/4)^x = 2^1 ==>(2^-2)^x = 2^1
 ==> 2^-2x = 2^1 ==> -2x= 1(-1) ==> x = - 1/2
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e) log7 = x ==> 7^x = 7 ==> 7^x = 7^1 ==> x = 1
         7
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 f) log4 = x ==> 1^x = 4  sem solução pq as bases são diferentes.
         1
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 g) log1/5 =  x ==> (1/5)^x = (1/5)^1 ==> x = 1
          1/5