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Mat logaritmos  005 exercicios
Mat logaritmos  005 exercicios
Mat logaritmos  005 exercicios
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Mat logaritmos 005 exercicios

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  • 1. EXERCÍCIOS SOBRE EXPONENCIAL E LOGARITMO1) Esboce o gráfico das seguintes funções: a) f(x) = 2x x x 1  d) f(x) =   - 3 1  2 b) f(x) =   2 e) f(x) = 3.2x c) f(x) = 2x + 2 x f) f(x) = 22) Resolva as seguintes equações exponenciais: x d) (2x )x + 4 = 32 1 a)   = 125 e) 4x + 1 – 9.2x + 2 = 0 5 b) 125x = 0,04 2x + 3  1 c) 5 3x-1 =   25 3) Calcule o valor do logaritmo dado. 1 a) log 8 64 b) log 4 64 c) log 64 8 d) log 2 64 e) log 2 1 f) log 2 2 g) log 1 8 h) log 1 81 2 34) Determine o domínio e faça um esboço do gráfico da função dada. a) f (x ) = log 1 x b) f (x ) = log 2 x c) f (x ) = ln( x + 1) 4 d) f (x ) = ln( x − 2) e) f (x ) = log 1 (− x ) f) f (x ) = − log 1 x 2 35) Reduza a expressão dada em um único logaritmo. 1 2 a) 4 log x + log y b) 5 ln x + ln y − 3 log 6 1 2 3 c) 3 log b ( x ) + log b (2y ) − 1 d) log 9 x + log 3 6 − 3 log 9 z 36) Sendo ln a = 2, ln b = 5, ln = −0,51 , calcule. 5 3b 2 a) ln(ab ) b) ln ab c) ln(a 2 b3 ) d) ln( ) 3 5 a7) Resolva as seguintes equações: a) ln x + ln 3 = ln 9 c) ln x − ln( x − 1) = ln 2 + ln( 3 − x ) b) ln (x − 2x 2 ) + ln 4 = 0 d) ln x 2 − ln x − ln 4 = 0
  • 2. RESPOSTAS DOS EXERCÍCIOS DO CÁLCULO ZEROEXPONENCIAL1a) 1b) 1c)1d) 1e) 1f)2a) V = {-3}  5 2e) V = {-2; 1} 2c) V = −   2  72b) V = −   3 2d) V = {-5; 1}LOGARTIMOS 13) a) 2; b) 3; c) ; d) –6; e) 0; f) 1; g) –3; h) –4. 24) a) D f = {x ∈ R / x > 0} b) D f = {x ∈ R / x > 0}
  • 3. c) D f = {x ∈ R / x > −1} d) D f = {x ∈ R / x > 2} e) D f = {x ∈ R / x < 0} f) D f = {x ∈ R / x > 0}  x3 2y 5) a) log( x 4 y ) ; b) ln( x 5 3 y 2 ) ; c) log b   ; d) log  36 x  .  b  9 3       z  76) a) 7; b) ; c) 19; d) 6,49. 2 37) a) 3; b) não existe; c) 2 ou ; d) 4. 2

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