06b Ecuaciones Logaritmicas Ejercicios Resueltos
Transcript of 06b Ecuaciones Logaritmicas Ejercicios Resueltos
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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
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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