lista-funcao exponencial

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UFRN - Universidade Federal do Rio Grande do Norte
ECT - Escola de Cieˆncia & Tecnologia
BCT - Bacharelado em Cieˆncias & Tecnologia
ECT1111 - Matema´tica Ba´sica
Lista 6 - Func¸o˜es Exponenciais, Equac¸o˜es Exponenci-
ais e Inequac¸o˜es Exponenciais
Livro: Geslson Iezzi. Fundamentos de Matema´tica Elementar - Vol. 1 - 7a ed. Ed.
Atual.
(60) Construa os gra´ficos cartesianos das seguintes func¸o˜es exponenciais:
(a) y = 3x (b) y = (1
3
)x (e) y = 10−x
(62) Construa os gra´ficos das func¸o˜es em R definidas por:
(a) f(x) = 21−x (b) f(x) = 3
x+1
2 (c) f(x) = 2|x|
(66) Construa os gra´ficos das func¸o˜es em R definidas por:
(a) f(x) = 2x − 3 (b) f(x) = (1
3
)x + 1 (c) f(x) = 2− 3x
(71) Resolva as seguintes equac¸o˜es exponenciais:
(a) 2x = 128 (b) 3x = 243 (c) 2x = 1
16
(d) (1
5
)x = 125 (e) ( 3
√
2)x = 8 (f) ( 4
√
3)x = 3
√
9
(g) 9x = 27 (h) 4x = 1
8
(i) ( 1
125
)x = 25
(j) ( 5
√
4)x = 1√
8
(k) 100x = 0, 001 (l) 8x = 0, 25
(m) 125x = 0, 04 (n) (2
3
)x = 2, 25
(72) Resolva as seguintes equac¸o˜es exponenciais:
1
(a) 23x−1 = 32 (b) 74x+3 = 49 (c) 112x+5 = 1
(d) 2x
2−x−16 = 16 (e) 3x
2+2x = 243 (f) 52x
2+3x−2 = 1
(g) 811−3x = 27 (h) 73x+4 = 492x−3 (i) 53x−1 = ( 1
25
)2x+3
(j) (
√
2)3x−1 = ( 3
√
16)2x−1 (k) 82x+1 = 3
√
4x−1 (l) 4x
2−1 = 8x
(m) 27x
2+1 = 95x (n) 8x
2−x = 4x+1
(76) Resolva as seguintes equac¸o˜es exponenciais:
(c) 23x−1.42x+3 = 83−x (e) 23x+2 : 82x−7 = 4x−1 (g) x+4
√
23x−8 = 2x−5
(h) 83x = 3
√
32x : 4x−1 (i)
x−1
√
3
√
23x−1 − 3x−7√8x−3 = 0 (j) √8x−1. x+1√42x−3 = 6√25x+3
(79) Resolva as seguintes equac¸o˜es exponenciais:
(e) 3.2x − 5.2x+1 + 5.2x+3 − 2x+5 = 2 (f) 2.4x+2 − 5.4x+1 − 3.22x+1 − 4x = 20
(81) Resolva as seguintes equac¸o˜es exponenciais:
(a) 4x − 2x − 2 = 0 (c) 4x − 20.2x + 64 = 0 (g) 22x + 2x+1 = 80
(h) 102x−1 − 11.10x−1 + 1 = 0 (j) 5.22x − 42x− 12 − 8 = 0
(92) Resolva as seguintes equac¸o˜es em R+:
(a) x2−3x = 1 (d) xx
2−7x+12 = 1 (e) xx
2−3x−4 = 1
(93) Resolva as seguintes equac¸o˜es em R+:
(c) x4−2x = x (d) x2x
2−5x+3 = x (e) xx
2−2x−7 = x
(116) Resolva as seguintes inequac¸o˜es exponenciais:
(b) (1
3
)x > 1
81
(e) ( 3
√
3)x ≤ 1
9
(f) (
√
2)x > 13√16
(l) ( 5
√
25)x <
1
4
√
125
(j) (0, 01)x ≤ 1
1000
(k) (0, 008)x > 3
√
25
2
(117) Resolva as seguintes inequac¸o˜es exponenciais:
(c) (0, 1)3−4x < 0, 0001 (e) (0, 42)1−2x ≥ 1 (f) 3x2−5x+6 > 9
(g) 2x
2−x ≤ 64 (h) (0, 3)x2−2x−8 ≥ 1 (i) 4x2+1 ≤ 321−x
(j) 27x
2−3 > 9 (k) (0, 01)2x
2+1 ≥ (0, 001)3x (l) 83x2−5x > 1
16
(m) (1
8
)x
2−1 < ( 1
32
)2x+1 (n) (
√
0, 7)x
2+1 ≥ ( 3√0, 7)2x+1
(121) Resolva as seguintes inequac¸o˜es exponenciais:
(b) (27x−2)x+1 ≥ (9x+1)x−3 (c) (2
3
)3x−2.(4
9
)2x+1 ≤ ( 8
27
)x−3
(e)
0, 043x+2.251−4x
0, 0083−x.1254−3x
> 1 (f)
x−1√
22x−3 : x+1
√
32 > 4
(g) x+1
√
0, 1. x+3
√
0, 01 < x+2
√
0, 001
(123) Resolva as seguintes inequac¸o˜es exponenciais:
(a) 2x−1 + 2x + 2x+1 − 2x+2 + 2x+3 > 240
(b) 3x+5 − 3x+4 + 3x+3 − 3x+2 < 540
RESPOSTAS
3
(71)
(a) S = {7} (b) S = {5} (c) S = {−4} (d) S = {−3}
(e) S = {9} (f) S = {8/3} (g) S = {3/2} (h) S = {−3/2}
(i) S = {−2/3} (j) S = {−15/4} (k) S = {−3/2} (l) S = {−2/3}
(m) S = {−2/3} (n) S = {−2}
(72)
(a) S = {2} (b) S = {−1/4} (c) S = {−5/2} (d) S = {5,−4} (e) S = {√6− 1,−√6− 1}
(f) S = {−2, 1/2} (g) S = {1/12} (h) S = {10} (i) S = {−5/7} (j) S = {5/7}
(k) S = {−11/16} (l) S = {2,−1/2} (m) S = {3, 1/3} (n) S = {2,−1/3}
(76)
(c) S = {2/5} (e) S = {5} (g) S = −{6,−2}
(h) S = {3/14} (i) S = ∅ (j) S = {2}
(79)
(e) S = {1} (f) S = {1}
(81)
(a) S = {1} (c) S = {2, 4} (g) S = {3}
(h) S = {0, 1} (j) S = {1, 2, 3/2}
(92)
(a) S = {1, 2/3} (d) S = {1, 3, 4} (e) S = {1, 4}
(93)
(c) S = {0, 1, 3/2} (d) S = {0, 1, 2, 1/2} (e) S = {1, 4}
(116)
4
(b) S = {x ∈ R|x < 4} (e) S = {x ∈ R|x ≤ −6} (f) S = {x ∈ R|x > −8/3}
(l) S = {x ∈ R|x < −3/10} (j) S = {x ∈ R|x ≥ 3/4} (k) S = {x ∈ R|x < −2/9}
(117)
(c) S = {x ∈ R|x < −1/4} (e) S = {x ∈ R|x ≥ 1/2}
(f) S = {x ∈ R|x < 1 ou x > 4} (g) S = {x ∈ R| − 2 ≤ x ≤ 3}
(h) S = {x ∈ R| − 2 ≤ x ≤ 4} (i) S = {x ∈ R| − 3 ≤ x ≤ 1/2}
(j) S = {x ∈ R|x < −
√
11
3
ou x >
√
11
3
} (k) S = {x ∈ R|1
4
≤ x ≤ 2}
(l) S = {x ∈ R|x < 1
3
ou x > 4
3
} (m) S = {x ∈ R|x < −2
3
ou x > 4}
(n) S = {x ∈ R|1
3
≤ x ≤ 1}
(121)
(b) S = {x ∈ R|x ≤ −1 ou x ≥ 0} (c) S = {x ∈ R|x ≥ −9
4
}
(e) S = {x ∈ R|x < −5
8
} (f) S = {x ∈ R|x < −1 ou 2
3
< x < 1}
(g) S = {x ∈ R| − 3 < x < −2 ou − 1 < x < 1}
(123)
(a) S = {x ∈ R|x > 5}
(b) S = {x ∈ R|x < 1}
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