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III. PHP PHP T N PH GII PHNG TRNH LOGARITH V d 1. Gii phng trnh
sau
a) 2 22log log (4 ) 12+ =xx x b) ( )3 93
42 log log 3 11 log
=
xxx
c) 2 25log (5 ).log 5 1=xx d) 3 32 22log log3
= x x
V d 2. Gii phng trnh sau
a) 2 23 log log (4 ) 0 =x x b) 1 4 3
5 4lg 1 lg+ =
+x x
c) 22log 64 log 16 3+ =x x d) 2 2log 2 2log 4 log 8+ =x x x
V d 3. Gii phng trnh sau
a) 2 2327log 3log 0 =xx x x b) 3 32 2log 2 3 log 2+ = x x
c) 2 4log 2log 2 log 2=x x x d) 22 2 23log 1 4 log 13log 5+ = +
x x x BI TP T LUYN: Bi 1. Gii cc phng trnh sau:
a) 512log 2 log5x
x = b) 29log 5 log 5 log 54x x x
x+ = +
c) 2 32 16 4log 14log 40log 0x x xx x x + = d) 3
3 2 3 23 1log .log log log
23x
x xx
= +
Hng dn gii:
a) ( )5 12log 2 log , 1 .5xx = iu kin: x > 0; x 1.
( ) ( )25 5 5 5 55
1 11 2. log 2 log 5 log 2 0 log 2log 1 0 log 1 5.2 logx
x x x x x xx
= + = + = = =
Vy phng trnh c nghim duy nht x = 5.
b) ( )29log 5 log 5 log 5, 2 .4x x x
x+ = +
iu kin: x > 0; x 1.
Ta c ( ) ( )2 2
1 5log 51 9 1 1 1 5 2 22 log 5 1 log 5 log 5 log 5 3. log 5 0 1
12 4 2 2 2 4 log 52 2
x
x x x x x
x
=
+ + = + + = =
T ta c 5 5log 5 5 5 5
log 5 1 5 5x
x
x x
x x
= = = = = =
Cc nghim ny u tha mn, vy phng trnh c hai nghim 55; 5.x x= = c) (
)2 32 16 4log 14log 40log 0, 3 .x x xx x x + =
Ti liu bi ging:
05. PHNG TRNH LOGARITH P4 Thy ng Vit Hng
Kha hc LTH mn Ton Thy ng Vit Hng (0985.074.831) Facebook:
LyHung95
Hc offline: S 11 ngch 98 ng 72 Tn Tht Tng (i din H Y H Ni) Hc
online: www.moon.vn
iu kin:
01022 1116 1
164 1 1
4
x
x x
x
x x
x
x
>
>
Khi ( ) ( ) ( ) ( )2 16 42 42 203 2log 42log 20log 0 0
log 2 log 16 log 4x x x x x xx x x
x x x + = + =
( )2 42 20 2 42 200 0, * .log log 2 log log 16 log log 4 1 log 2
1 log 16 1 log 4x x x x x x x x xx x x
+ = + =+ + + + + +
t ( ) ( )( ) ( )( ) ( )( )1 21 10log 2, * 0 1 4 1 2 21 1 1 2 10
1 1 4 01 1 4 1 2x
t t t t t t tt t t
= + = + + + + + + + =+ + +
( ) ( )2 2 2 22
8 6 1 21 2 3 1 10 4 5 1 0 6 7 10 0 56
tt t t t t t t t
t
= + + + + + + + = = =
Vi 22 log 2 2 2 2.xt x x= = = =
Vi
65 5 6 656 6 5 5
x 55 5 1
t log 2 x 2 x 2 x 26 6 64
= = = = = =
i chiu vi iu kin ta c nghim ca phng trnh l 5
11; 2; .64
= = =x x x
// Thy gii thiu mt nghim x = 1, cc em kim tra li ch no nh???
d) ( )3
3 2 3 23 1log .log log log , 4 .
23x
x xx
= +
iu kin: x > 0.
( ) ( ) ( ) ( )33 2 3 3 2 3 2 3 21 1 1 1 14 1 log .log log log 3
log 1 log .log 3log log2 2 2 2 2x x x x x x x x = + + = + 2 2 3 3 2
2 2 3 3
1log log .log 3log log 0 log 2log .log 6log 02
x x x x x x x x x = =
( ) ( )2 3 3log 1 2log 6log 0, * .x x x = Do 3 3 2log log 2.logx
x= nn ( ) ( ) ( )2 3 3 2 2 3 3* log 1 2log 6log 2.log 0 log 1 2log
6log 2 0x x x x x = =
23
3 33 3
1 1log 01 6log 2 1 3 3log log1 2log 6log 2 0
2 2 64 8
x xx
xx x
= = =
= = = =
Cc nghim ny u tha mn iu kin, vy phng trnh c hai nghim 31; .8
x x= =
Bi 2. Gii cc phng trnh sau:
a) ( ) ( ) 61log1log 2322232 =++++ + xxxx b) ( ) 34log2log 22 =+
xx
c) ( ) 33logloglog 433313 =++ xxx d) 4
7log 2 log 06
+ =x x
Bi 3. Gii cc phng trnh sau:
a) 225log.3logloglog 9535 =+ xx b) ( ) ( )1log22log113log 2
32 ++=+
+
xxx
c) ( ) ( )32log44log 1212 =+
+xx x d) 33loglog.4 9 =+ xx
Bi 4. Gii cc phng trnh sau:
