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a) \(3^{2x-1}=243\)
\(\Leftrightarrow3^{2x-1}=3^5\)
\(\Leftrightarrow2x-1=5\)
\(\Leftrightarrow2x=5+1\)
\(\Leftrightarrow2x=6\)
\(\Leftrightarrow x=\dfrac{6}{2}\)
\(\Leftrightarrow x=3\)
Vậy \(x=3\)
b) \(\left(3^x\right)^2:3^3=\dfrac{1}{243}\)
\(\Leftrightarrow3^{2x}:3^3=\dfrac{1}{3^5}\)
\(\Leftrightarrow3^{2x}:3^3=3^{-5}\)
\(\Leftrightarrow3^{2x-3}=3^{-5}\)
\(\Leftrightarrow2x-3=-5\)
\(\Leftrightarrow2x=-5+3\)
\(\Leftrightarrow2x=-2\)
\(\Leftrightarrow x=-\dfrac{2}{2}\)
\(\Leftrightarrow x=1\)
Vậy \(x=1\)
c) \(2^{3x+2}=4^{x+5}\)
\(\Leftrightarrow2^{3x+2}=\left(2^2\right)^{x+5}\)
\(\Leftrightarrow2^{3x+2}=2^{2\left(x+5\right)}\)
\(\Leftrightarrow3x+2=2\left(x+5\right)\)
\(\Leftrightarrow3x+2=2x+10\)
\(\Leftrightarrow3x-2x=10-2\)
\(\Leftrightarrow x=8\)
Vậy \(x=8\)
d) \(3^{x+1}=9^x\)
\(\Leftrightarrow3^{x+1}=\left(3^2\right)^x\)
\(\Leftrightarrow3^{x+1}=3^{2x}\)
\(\Leftrightarrow x+1=2x\)
\(\Leftrightarrow2x-x=1\)
\(\Leftrightarrow x=1\)
Vậy \(x=1\)
1) 2x . 4 = 128
2x = 128 : 4
2x = 32
2x = 25
=> x = 5
2) (2x + 1)3 = 125
(2x + 1)3 = 53
=> 2x + 1 = 5
2x = 5 - 1
2x = 4
x = 2
các bài khác bạn tự làm nha
a, 3.(x-9)+15=12+243:32
3x-27+15=12+243:9
3x-12=12+27
3x=12+12+27
3x=51
x=17
b, (3x-48).6=33.22+32.23-122
18x-288=32.3.22+32.22.2-(3.2.2)2
18x-288=32.3.22+32.22.2-32.22.22
18x-288= 32.22.(3+2-22)
18x-288= 9.4.(3+2-4)
18x-288=36.1
18x-288=36
18x=36+288
18x=324
x=18
\(5x+2x=6^2-5^0\)
\(7x=36-1\)
\(7x=35\)
\(x=5\)
vậy \(x=5\)
\(5x+x=150:2+3\)
\(6x=75+3\)
\(x=78:6\)
\(x=13\)
vậy \(x=13\)
những câu sau tương tự
1) 5x + 2x = 6^2 - 5^0
=> 7x = 36 - 1 = 35
=> x = 35 : 5 = 5.
Vậy x = 5
2) 5x + x = 150 : 2 + 3
=> 6x = 75+3 = 78
=> x = 78 : 6 =13.
Vậy x = 13
3) 6x + x = 5^11 : 5^9 - 3^1
=> 7x = 5^2 -3 = 25 - 3 = 22
=> x = 22 : 7 = 22 / 7.
Vậy x = 22/7
4) 5x + 3x = 3^6 : 3^3 .4 + 12
=> 8x = 3^3 .4 + 12= 27.4 + 12 = 108 + 12 =120
=> x = 120 : 8 = 15.
Vậy x = 15
5) 4x + 2x = 68 - 2^19 : 2^16
=> 6x = 68 - 2 ^3 = 68 - 8 =60
=> x = 60 : 6 =10.
Vậy x = 10
6) 5x + x = 39 - 3^11 : 3^9
=> 6x = 39 - 3^2 = 39 - 9 = 30
=> x = 30 : 6 =5.
Vậy x =5
7) 7x - x = 5^21 : 5^19 + 3. 2^2 - 7^0
=> 6x = 5^2 + 3.4 - 1 = 25 + 12 - 1 = 36
=> x = 36 : 6 = 6.
Vậy x = 6
8) 7x - 2x = 6^17 : 6^15 + 44 : 11
=> 5x = 6^2 + 4 = 36 + 4 = 40
=> x = 40 : 5 = 8 .
Vậy x = 8
a) \(\left(2x-1\right)^3=125\)
\(\left(2x-1\right)^3=5^3\)
\(=>2x-1=5\)
\(=>2x=6\)
\(=>x=3\)
vay \(x=3\)
a) (2x-1)3 = 125
=> 2x-1 = 5
2x = 5+1
2x = 6
x = 6:2
x = 3
Bài b,c mình tính phần thập phân nhiều quá khó tính
d) 3x.3.32=243
=> 3x.31+2 = 35
3x.33=35
3x=35:33 ( 35-3 )
3x = 32 ( 32=9 )
<=> x = 9:3
x = 3
So sánh :
a) 2711 và 818
2711 = (33)11 = ...7
818 = (92)8 = ...1
Vậy ...7 > ...1 nên 2711 > 818
b) 6255 và 1257
6255 = (252)5 = ...5
1257 = (53)7 = ...5
Vì trường hợp 2 chữ số tận cùng = nhau nên chúng ta so sánh số mũ
6255 = (252)5 = 2510 = (52)10 = 520
1257 = (53)7 = 521
Vì 520 < 521 (20<21) Nên 6255 < 1257
c) 32n và 23n
32n = (32)n = ...9
23n = (23)n = ...8
Vì ...9 > ...8 nên 32n > 23n
d) 2918 và 7913
2918 >2518=539=(53)13 <=>12513>7913
e) 339 và 1121
=> 1121 > 339 =(32)21 => 342>339
\(1,2x+3x-4x=\left(-2\right)^3\)
<=>\(x=-8\)
\(2,x-2x=4^2+4^0\)
<=>\(-x=16+1\)
<=>\(-x=17\)
<=>\(x=-17\)
\(3,2^3x-3^2x=|12-21|\)
<=>\(-x=9\)
<=>\(x=-9\)
\(4,x-45=2x+54\)
<=>\(x-2x=54+45\)
<=>\(-x=99\)
<=>\(x=-99\)
\(5,5x-12+23=6^7:6^5\)
<=>\(5x+11=6^2\)
<=>\(5x+11=36\)
<=>\(5x=25\)
<=>\(x=5\)
2x - 138 = 23 . 32
=> 2x - 138 = 72
=> 2x = 72 + 138
=> 2x = 210
=> x = 105
10 + 2x = 43 . 42
10 + 2x =1024
2x = 1024 - 10
2x = 1014
x = 507
(3x - 24) . 73 = 2.74
3x - 24 = 2 . 74 : 73
3x - 16 = 14
3x = 14 + 16
3x = 30
x = 10
x4 = 16
=> x4 = 24
=> x = 2
\(5x+2x=6^2-5^0\Leftrightarrow5x+2x=6^2-1\)
\(\Leftrightarrow5x-2x=36-1\Leftrightarrow5x-2x=35\Leftrightarrow x\left(5+2\right)=35\)
\(\Leftrightarrow7x=35\Leftrightarrow x=35:7\Leftrightarrow x=5\)
\(5x+x=150:2+3\Leftrightarrow5x+x=75+3\)
\(\Leftrightarrow5x+x=78\Leftrightarrow x\left(5+1\right)=78\Leftrightarrow x6=78\)
\(\Leftrightarrow x=78:6\Leftrightarrow x=13\)
a) 5x + 2x = 62 - 50
7x = 35 => x = 5
b) 5x + x = 150 : 2 + 3
6x = 78 => x = 13
c) 6x + x = 511 : 59 + 31
7x = 28 => x = 4
d) 5x + 3x = 36 : 33 x 4 + 12
8x = 120 => x = 15
e) 4x + 2x = 68 - 219 : 216
6x = 60 => x = 10
f) 5x + x = 39 - 311 : 39
6x = 30 => x = 5
g) 7x - x = 521 : 519 + 3 x 22 - 70
6x = 36 => x = 6
h) 7x - 2x = 617 : 615 + 44 : 11
5x = 40 => x = 8
a. 8x+2x =25. 2 mũ 2
8x+2x=100
(8+2)x=100
10x=100
x=100:10
x=10
b.5x+2x=35
(5+2)x=35
7x=35
x=35:7
x=5
a) 3x = 243
=> 3x = 35
=> x = 5
b) 5.52x+1 = 625
=> 52x+2 = 54
=> 2x+2 = 4
=> 2x = 2
=> x = 1
c) (6-3x)(311-3x-243)=0
\(\Rightarrow\left[{}\begin{matrix}6-3x=0\\3^{11-3x}-243=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x=6\\3^{11-3x}=243=3^5\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\11-3x=5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\3x=6\end{matrix}\right.\Rightarrow x=2\)
d) (12-2x)3=23.33
=> (12-2x)3=(2.3)3
=> (12-2x)3=63
=> 12-2x=6
=> 2x=6
=> x = 3