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Ecuaciones Exponenciales y Logaritmicas

1) Resolver las siguientes ecuaciones:

a) (1 + x).√4 = 2x b) 2(x - 1) = 2x c) 5(x + 1) + 5x = 750 d) (9/4)(x + 1).(8/27)(x - 1) = 2/3

e) 3(x + 1) + 2.3(2 - x) - 29 = 0 f) 4x+1 + 2x+3 = 320 g) 5x + 5x+2 + 5x+4 = 651

| 2) Resolver el sistema: | 2x - 4 ².y = 0 |

| |x - y = 15 |

| 3) Resolver el sistema: | 22.x + 5.y = 2 |

| |2-.x + y = 8 |

| 4) Resolver el sistema: | 2x + 2y = 24 |

| | 2x.2y = 128 |

5) Calcular:

a) 8 log7 7 b) 3 log32 2 c) 5 log3 7 d) 3 log1/81 9 e) 25 log25 5 f) 9 log9 h

g) logx 2 = 1/3 h) logx 5 = 1/3 i) logx 5 = -1/3 j) logx 0,25 = 2

k) logx 16 = -2 l) log4 x = 5/2 m) log2 (x ² + 2.x) = 3

6) Resolver las siguientes ecuaciones:

a) log2 (x ² + 1) - log2 x = 1

b) log2 (9.x ² - 20) - log2 x - log2 6 = 2

c) log2 (x ² + 1) - log2 x = log 2

d) log4 x - log4 (x - 1) = 1

e) log4 x - log2 x = 9

f) log2 x - 3.[log8 (x + 1)]/2 = 2

g) log2 (x + 1)/(x - 1) = log2 3/2

h) log (x³ - 6.x ² + 11.x - 5) = 0

i) log³ x + log9 x = log81 x + 5/2

j) xlog x = 108

k) log (2.n + 1)/(n - 1) = 0

l) [log 2.x] / [log (4.x - 15)] = 2

m) log1/2 1/16 + 2.log3 (x - 3).log3 (x + 2) = log3 ²(x - 3).log3 ²(x + 3)

d) 1/ (5 - log x) + 2 / (1 + log x) = 1

e) log x³ - 12 / log x = 5

f) log √7.x + 5 + (1/2).log (2.x + 7) = 1 + log 4,5

g) xlog (x - 1) = 100

h) (xlog √x)1/2 = 10 → R: x1 = 100 y x2 = 1/100

i) [log (35 - x³)] / [log (5 - x)] = 3

7) Resolver las siguientes ecuaciones:

a) 3x + 1 + 18/3x = 29 b) xx ² - 7.x + 12 = 1 c) 72.x - 6.7x + 5 = 0

d) (2.√12 + 3.√3 + 6.√1/3)2/5 = (32.x ² - 2.x - 2)½ → R: x1 = 2 y x2 = -1

e) 3(x + 1) + 2.3(2 - x) - 29 = 0

8) Sabiendo el log 2 = 0,301 y el log 3 = 0,477, calcular:

a) log √30 b) log 5 c) log 0,27 d) log 0,0128

9) Resolver

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Hallar x logx (3x+4) + logx (x2 – 9 ) = logx (3x -5) + 2

Hallar x log 2 + log (11 – x2 ) = 2 – logx (5 – x)

Resolver:

log ( x + 1 ) / log ( x ( 1 ) = 2 R : 3

log ( x ( 7 ) / log ( x ( 1 ) = 0,5 R : 10

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