Question

dados log 2 = 0,30; log 3 =0,48 e o log 5= 0,70, calcule: a) log 20; b) log 0,0002; c) log 0,3; d) log 18; e) log 45; f) log 250. LOG: LOGARITMO

Answer 1

log 2 = 0,30; log 3 =0,48 e o log 5= 0,70, calcule:

a) log 20 = log(2².5) = log2² + log5 = 2log2 + log5
 
2(0,30)+0,70==>0,60+0,70 ==> 1,30
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b) log 0,0002 = log(2.10^-4) = log 2 + log10^-4 = log2 - 4log10

0,30 - 4.1 ==> - 3,70
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c) log 0,3 = log(3.10^-1) = log3 - 1. log10 = 0,48 - 1 ==> - 0,52 
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d) log 18 = log (2.3²) = log2 + log3² = log2 + 2log3 
 
0,30+ 2.(0,48) ==> 0,30 + 0,96==> 1,26
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e) log 45 = log (3².5) = log3² + log5 = 2log3 + log5

2(0,48) + 0,70 ==> 0,96+0,70 ==> 1,66
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f) log 250 = log(2 . 5³) = log2 + log5³ = log2 + 3log5

0,30+ 3(0,70) = 0,30 + 2,10 ==> 2,40

Answer 2

a) log 20 = 1,30

b) log 0,0002 = - 3,70

c) log 0,3 = - 0,52

d) log 18 = 1,26

e) log 45 = 1,66

f) log 250 = 2,40

Explicação:

a) log 20 = log(2 . 2 . 5) =

log 2 + log 2 + log 5 = 0,30 + 0,30 + 0,70 = 1,30

 

b) log 0,0002 = log(2.10⁻⁴) =

log 2 + log10⁻⁴ = log 2 - 4.log 10  =

0,30 - 4.1 = 0,30 - 4 = - 3,70

c) log 0,3 = log 3/10 =

log 3 - log 10 = 0,48 - 1 = - 0,52

d) log 18 = log (2 . 3 . 3) =

log 2 + log 3 + log 3 = 0,30 + 0,48 + 0,48 = 1,26

 

e) log 45 = log (3. 3 . 5) =

log 3 + log 3 + log 5 = 0,48 + 0,48 + 0,70 = 1,66

f) log 250 = log(2 . 5 . 5 . 5) =

log 2 + log 5 + log 5 + log 5 =

0,30 + 0,70 + 0,70 + 0,70 = 2,40

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