ECUACIONES 1 BCT

Luisa Muoz 1

ECUACIONES LOGARTMICAS

Actividades resueltas

1.- Resuelve las siguientes ecuaciones logartmicas:

1) log x = -1 10-1 = x x = 01

2) 2logx log 4x = -2

log x2 log 4x = -2 log 2x

4x= log 10-2

2x 14x 100

= 100 x2 4x = 0 4x ( 25x 1) = 0

x = 0 (n vlida)

x = 1

25=004

3) log x = 3 103 = x x = 1000

4) log (x2 4x + 3) = log (3 2x) x2 4x + 3 = 3 2x x2 2x = 0 x = 2, x = 0

x = 0 log 3 = log 3

x = 2 log -1 = log -1 (No vlida)

5) log 2 x = -2 2-2 = x x = 0,25

6) log (x 2) + 1 = log (x 1)+log 2 Log[10(x 2)] = log[ 2(x 1)] 10(x 2) = 2(x 1) 5x 10 = x 1 4x = 9 x = 9/4

7) 2log x = -10

Log x2 = -10 10-10 = x2 x = 10-5

8) 3 log x log 32 = log x log 2

log 3x

32 = log x

2

3x

32=

x

2 x3 16x = 0 x(x2 16) = 0 x = 0 ; x = 4

Solucin vlida: x = 4

ECUACIONES 1 BCT

Luisa Muoz 2

9) log x + log 50 = 3

Log 50x = log 1000 50x = 1000 x = 20

10) log 3x + 1 - log 2x -1 = 1- log 5

3x 1log log22x 1

+=

3x 1 22x 1

+=

3x 1 42x 1

+=

3x + 1 = 8x 4 5x = 5 x = 1

11) log x = 1 + log (22 x)

Log x = log (220 10x) x = 220 10x 11x = 220 x = 20

12) log 2 log (x 3 ) log 2x+ =

log (2x 6) log 2x = 2(x 3 ) 2x = 4(x 3)2 = 2x 2x2 12x + 18 = x

2x2 13x + 18 = 0 x = 13 169 144 13 54 4

= x =

184