logaritmos (1)

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1) Determine o valor de
a) E = log log . loglog1000 9 125 164 2 4 53− + . Resp : 4
11
 
b) E = log log log2
3
8 4
3
64 1
27
64
− + . Resp : –1 
a) E = ( )log , log loglog0 001 9 813 3 3 4 3+ − . Resp : 23 
2) Dado log 2 = a , calcule x = log 4 + log 6 + log 
2
3
 + log 0,25 . Resp : 2a
3) Considere log 2 ≅ 0,3 e log 3 ≅ 0,5 , determine o valor da expressão :
S = log 45 + 16log 2 - ( )log log4
3
4 1000 . Resp : 10,7 
4) Sendo log8 a = m , calcule o valor de loga1024 . Resp: 
10
3m
5) Resolva , em R , as equações :
a) ( ) ( )log log4 410 5 2x x+ + − = . Resp : {6} 
b) ( ) ( )log log2 2 21 1 1x x+ = − + . Resp : {3} 
c) log (x2 - 8x) - log ( -x2 – x + 6) = log 
3
2
 . Resp : { -1} 
d) ( )log log1
2
2
1
2
2 2x x x+ − = − . Resp : {2} 
e) ( ) ( ) ( )4log12log22log 3
3
1
2
3 −=+++− xxxx . Resp : {6} 
f) log2 (x2+2x-7) - log2 (x-1) = 2 . Resp : {3}
6) Resolva as equações :
a) log3 x + log3 (x-2) = 3 Resp: 1+2 7
b) log (3x2 + 7) – log (3x – 2) = 1 Resp: 1 ou 9
c) 
2
1
−
−
log
log
x
x - 3 = 0 Resp: 10
d) 3 log82 x + 3 = log 8 x10 Resp : 2 ou 512
e) log2 x + log 2 x + log 
1
2 x = 8 Resp: 16
7) Determine o valor de ∑∑
==
−
9
1
10
1
loglog
ji
ji . Resp : 1
8) Esboce os gráficos e determine a imagem e o domínio das seguintes funções:
a) y = log2(x+2) b) y = log 
1
2 x  + 2 c) y = 1 + 3 . log2 2x
 1/2
Bornattos
Stamp
9) Determine o domínio de y = 2log
2
1 +



x . Resp: ]0;4]
10) Resolva as inequações :
a) ( )log1
2
5 3− >x . b) ( )log1
3
2 2 1x x− ≥ − . c) ( )log log1
2
1
2
1 1x x+ − ≤ − .
Resp: a) 

 5,
8
39
 b) [ [ ] ]3,20,1 ∪− c) [ [+ ∞,2 
11) Resolva as inequações :
a) ( ) 010log 2
3
1 ≤− x Resp: [-3;3]
b) 2 . log (x-4) ≤ log 4 Resp: ]4;6]
c) log2x – log x3 –4 < 0 Resp: ]1/10;10000[
d) log3(x-1) – log9(x-2) ≥ log9



+
3
22x
 Resp: ]2;7/3]
 2/2