03 aula de função logarítmica
TRANSCRIPT
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03. (UFSCar-SP) O domínio de definição da funçãof(x) = logx – 1 (x2 – 5x + 6) é:a) x < 2oux > 3b) 2 < x < 3c) 1 < x < 2oux > 3d) x < 1oux > 3e) 1 < x < 3Resoluçãof(x) = logx – 1 (x2 – 5x + 6)D = {xIR / 1< x < 2 ou x > 3}Resposta: CExercícios Resolvidos01. (Vunesp) Sejamx ey números reais, comx > y. Se log3(x – y) = m e (x + y) = 9,
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determine:a) o valor de log3(x + y);b) log3(x2 – y2), em função de m.Resoluçãoa) log3(x + y) = log39 = 2.b) log3(x2 – y2) = log3 [(x + y) · (x – y)] =log3 (x + y) + log3 (x – y) = m + 2. 02. Se log 2 = x e log 3 = y, então log 72 é igual a:a) 2x + 3yb) 3x + 2yc) 3x – 2yd) 2x – 3ye) x + yResoluçãolog72 = log(23 · 32) = log23 + log32 == 3 · log2 + 2 · log3 = 3x + 2yResposta:B03. (Fuvest-SP)Sex = log47ey = log1649,então x – y é igual a:a) log4 7b) log167c) 1d) 2e) 0Resoluçãox – y = x – x = 0Resposta:E
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04. (UFF-RJ) Sendo loga = 11, log b = 0,5, log c = 6 e log= x, o valor de x é:a) 5b) 10c) 15d) 20
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e) 25ResoluçãoResposta:BExercícios Resolvidos
01. (PUC-SP) Um estudante quer resolver a equação 2x = 5, utilizando uma calculadora quepossui a tecla log x. Para obter um valor aproximado de x, o estudante deverá usar a calculadorapara obter os seguintes números:a) log 2, log 5 e log 5 – log 2b) log 2, log 5 e log 5 : log 2c) log 2, log 5 e log 25d) 5/2 e log 5/2e) e logResoluçãoAplicando logaritmo com base 10 nos dois membros temos:log 2x = log 5x · log 2 = log 5⇒ x =Resposta:B02.(FGV-SP)Aequaçãologarítmica
log2 (x + 1) + log2 (x – 1) = 3admite:a) uma única raiz irracional.b) duas raízes opostas.c) duas raízes cujo produto é – 4.d) uma única raiz e negativa.e) uma única raiz e maior do que 2.ResoluçãoCondição de existência:x + 1 > 0⇒ x > – 1 ; x – 1 > 0⇒ x > 1.Assim x > 1log2 (x + 1) · (x – 1) = 3log2 (x2 – 1) = 3⇒ x2 – 1 = 23⇒ x 2 – 1 = 8x = 3Resposta:E
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03. (Cesgranr
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io-RJ) Se
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log x representa
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o logaritmo
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decimal do
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número positi
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vo x, a
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soma das
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raízes delo
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g2 x – log
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x2 = 0 é:
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a) – 1b) 1
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c) 20d) 100
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e) 101
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Resolução
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Condição de
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existência: x > 0
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log2 x – log x2 =
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0log2 x – 2
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log x = 0
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Fazendo log x
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= y, obteremos:
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y2 – 2y = 0y(y
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– 2) = 0y = 0 ou
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y = 2log x = 0x
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= 1log x
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= 2x = 100
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a soma das
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raízes será 101.
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S = {101}
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Resposta:E
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Exercícios
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Resolvidos
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01. (FCMSC
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-SP) São dado
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s:log15 3 = aelo
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g15 2 = b. O
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valor de
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log10 2 é:a)
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b) c) d)
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e)
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Resolução
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Resposta:B
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02. (FGV-SP)
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O produto
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(log92) · (lo
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g25) · (log53)
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é igual a:
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a) 0b)c) 10
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d) 30e)
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Resolução
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x=
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Resposta:B
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03.A
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expressão
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é
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equivalente a:
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a) log250
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b) log2 10
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c) log2 5
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d) log2 2
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e) log2
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Resolução
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log2 3 · log3 5
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· log5 10 =
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log2 10e
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Portanto
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log2 10 + log2
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= log2 10
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Resposta:B