Chuyên đề luyện thi đại học: Phương pháp đưa về cùng cơ số

Chuyên đề luyện thi đại học: Phương pháp đưa về cùng cơ số 
Nguyễn Đức Toàn Thịnh – GV Trường THPT Trung Giã Trang 1 
Giải phương trình-bất phương trình: 
1) log3x + log9x + log27x = 11 2) 0)3(log 222 =−+ xx ( ) ( )1-xlog1xlog 3)
2
1
2
2 =− 
4) ( ) 441log 2
2
1 ≤−−+ xx 5) log3x.log9x.log27x.log81x = 3
2 6) ( ) 05loglog 24
2
1 >−x 
7) 






−=+




 + x
x
1
327lg2lg3lg
2
11 8) 
8
3log33log31log 222 −+=x 9) ( ) 012log 2
5
1 ≤+−− xx 
10) ( )
x
xx
4
4 log
210log.2log21 =−+ 11) 1
3
19log 23 −≥




 +−− xx 12) logx(2x2 – 7x +12) = 2 
13) log2x.log3x = log2x2 + log3x3 – 6 14) 6logloglog
3
133 =++ xxx 15) xx 73 loglog ≤ 
16) 1log32log
3
1
3
1 +=+− xx 17) 5
1log25log2 5 x=− 18) 02log3
1log 3
5
1 =




 −x 
19) 0
4
2log
2
1log 2
2
1 =−+




 −
xx 20) 
xx coslog
2
1sinlog
2
1
2
1
155 1555
++
=+ 21) 1
11
1log2 =






−−x
22) ( ) 944log2log 2323 =++++ xxx 23) log2x + log3x + log4x = log10x 24) log3(5x2 + 6x + 1) ≤ 0 
25) log4(log2x) + log2(log4x) = 2 26) log2(4.3x - 6) - log2(9x - 6) = 1 27) ( ) 1log296log 32
2
8 −+− = xxx x 
28) 6lg5lg)21lg( +=++ xx x 29) log3(4.3x – 1) = 2x – 1 30) 1)(loglog
2
1
3
1 −=x 
31) )12(log.3log21
log
2log21
9
9
9 x
x x
−=−
+
 32) ( ) 13log25log
3
1
82 =−+− xx 33) 2
1
2
12log4 −<+
−
x
x 
34) ( ) ( )3 21 3
3
1) log 2 x x 2 log 2x 2 0  + − + + = 
 35) 3logloglog
2
142 =+ xx 36) 11
32log3 <−
−
x
x
37) )1(log)1(log)1(log 543 +=+++ xxx 38) 2log2log.2log 42 xxx = 39) log2(|x+1| - 2)= -2 
40) ( )( ) 5lg2lg210lg 21lg 2 −=−− xx 41) ( ) 0
2
6log1log
3
13 =−
+−
x
x 42) 
( ) 3
40lg
11lg
3
=
−
++
x
x
43) ( ) ( ) 21log31log 2222 =−++−− xxxx 44) 1 + lg(1 + x2 –2x) – lg(1+x2) = 2lg(1–x) 
45) xxx
x 2
3
323 log2
1
3
loglog.3log +=−




 46) ( ) xxxx lg
2
16lg
2
1
3
1lg
3
4lg −+=




 −−




 + 
47) ( ) 2lg
2
5lg1lg
2
1lg2 +




 +=−−




 + xxx 48) 3
59
27log)39(log
223
2
3
1 −
−+−
>+−
xxx
xx 
49) 
2
11loglog3log 312525
3
5 =++ xxx 50) ( ) 3log2
1log.265log 33
122
9 −+
−
=+− − xxxx 
51) log2(x2+3x+2) + log2(x2+7x+12) = 3+ log23 52) 1log)1(log).1(log 26
2
3
2
2 −−=−+−− xxxxxx 
53) ( )[ ]{ }
2
1log31log1log2log 2234 =++ x 54) 2 + lg(1 + 4x
2 – 4x) – lg(19 + x2) = 2lg(1 – 2x) 
55) 2)23lg()32lg( 22 =−−− xx 56) log2(x2 + 3x + 2) + log2(x2 + 3x + 12) = 3 + log23 
57) lg5 + lg(x+10) =1–lg(2x–1)+lg(21x–20) 58) 2log3(x–2)2+(x–5)2logx–23 = 2logx–29 + (x–5)2log3(x – 2) 
59) )1(log1)21(log 55 ++<− xx 60) (x – 4)
2log4(x –1)–2log4(x–1)2 =(x–4)2logx-1 4–2logx-116 
61) ( ) ( )1x2log1-xlog 3222 ++= x 62) log2(25x + 3 –1) = 2 + log2(5x + 3 + 1)