EJERCICIOS DE LOGARITMOS.
Enviado por mafali • 21 de Noviembre de 2014 • Tareas • 1.209 Palabras (5 Páginas) • 202 Visitas
EJERCICIOS DE LOGARITMOS
1 ) 10 log ( 7 ) = 7
2 ) 10 2 + log ( 3 ) = 10 2 × 10 log ( 3 ) = 100 × 3 = 300
3 ) log 8 ( 64 ) + log 4 ( 64 ) = log 8 ( 8 2 ) + log 4 ( 4 3 ) = 2 + 3 = 5
4 ) log 4 ( 8 ) + log 4 ( 2 ) = log 4 ( 8 × 2 ) = log 4 ( 16 ) = 2
5 ) log 9 ( 243 ) – log 9 ( 81 ) = log 9 ( 243 ÷ 81 ) = log 9 ( 3 ) = 0,5
6 ) log 7 ( 2 ) + log 7 ( 0,5 ) = log 7 ( 2 × 0,5 ) = log 7 ( 1 ) = 0
7 ) log 5 ( 375 ) – log 5 ( 3 ) = log 5 ( 375 ÷ 3 ) = log 5 ( 125 ) = 3
8 ) log 0,25 ( 16 ) = log 0,25 ( 4 2 ) = log 0,25 ( 0,25 – 2 ) = – 2
9 ) log 5 ( 8 × 10 – 3 ) = log 5 ( 2 3 × 10 – 3 ) = log 5 ( 0,5 – 3 × 10 – 3 ) =
log 5 ( 5 – 3 ) = – 3
10 ) log 16 ( 32 ) = log ( 32 ) / log ( 16 ) = log ( 2 5 ) / log ( 2 4 ) = 5 / 4 = 1,25
11 ) log 81 ( 27 ) = log ( 27 ) / log ( 81 ) = log ( 3 3 ) / log ( 3 4 ) = 3 / 4 = 0,75
12 ) log 4 ( 3 x + 1 ) = 2
3 x + 1 = 4 2 = 16
x = 5
13 ) log x ( 343 ) = 3
x 3 = 343
x = 7
14 ) log x + 1 ( 64 ) = 2
( x + 1 ) 2 = 64
x + 1 = 8
x = 7
15 ) log 3 ( 4 x + 1 ) = 4
4 x + 1 = 3 4 = 81
x = 20
16 ) log x ( 5 x – 6 ) = 2
x 2 = 5 x – 6
x 2 – 5 x + 6 = 0
( x – 2 ) ( x – 3 ) = 0
x 1 = 2
x 2 = 3
Si log ( 2 ) = a , log ( 3 ) = b y log ( 7 ) = c , entonces:
1 ) log ( 6 ) = log ( 2 × 3 ) = log ( 2 ) + log ( 3 ) = a + b
2 ) log ( 49 ) = log ( 7 2 ) = 2 log ( 7 ) = 2 c
3 ) log ( 5 ) = log ( 10 / 2 ) = log ( 10 ) – log ( 2 ) = 1 – a
4 ) log ( 2 ) = log ( 2 0,5 ) = 0,5 log ( 2 ) = 0,5 a
5 ) log ( 12 ) = log ( 2 2 × 3 ) = log ( 2 2 ) + log ( 3 ) = 2 log ( 2 ) + b = 2 a + b
6 ) log ( 700 ) = log ( 7 × 100 ) = log ( 7 ) + log ( 100 ) = c + 2
7 ) log ( 0,5 ) = log ( 2 – 1 ) = – log ( 2 ) = – a
8 ) log ( 3 / 7 ) = log ( 3 ) – log ( 7 ) = b – c
9 ) log ( 0,125 ) = log ( 2 – 3 ) = – 3 log ( 2 ) = – 3 a
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