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b, 2x = 42x45 /8
2x = 16x45 /8
2x = 2x45
2x = 2x(22)5
2x = 2x210
2x = 211
=> x = 11
3\(^x\) . 3 = 43
=> 3\(^{\left(x+1\right)}\) = 43
=> Không có giá trị x thoả mãn .
49 . \(7^x\) = 2041
7\(^2\) . 7\(^x\) = 2041
7\(^{\left(x+2\right)}\) = 2041
=> \(7^{\left(x+2\right)}\) = 7\(^4\)
=> x + 2 = 4
=> x = 2
1) 3^4.2+2^3.5-7(5^7:5^5)
=3^4.2+2^3.5-7.5^2
=81.2+8.5-7.25
=162+40-175
=202-175=27
2) 5.2^2.2^3-4(5^8:5^6)
=5.4.8-3.5^2
=160-100=60
3) (3^5.3^7):3^10+5.2^4-7^3:7
=3^12:3^10+5.16-7^2
=3^2+80-7^2
=9+80-49=40
4) 15:(3^5:3^4)-2^9:2^7
=15:3-2^2
=5-4=1
5) 5.3^5:(3^8:3^5)-2^3.5
=5.3^5:3^3-8.5
=5.3^2-40
=5.9-40
=45-40=5
a)5x-2 - 32 = 24 - ( 28 * 24- 210 * 22 )
=> 5x-2-32=16
=> 5x-2=25
=> (5x)2=25
=> 5x=5
=> x=1
b) ( 3 * x - 24 ) * 73 = 8 * 74
=> (3.x-16)=8.74:73
=> 3x-16=56
=> 3x=72
=> x=24
c) x15 = x
=> x15:x=1
=> x14=1
=> x=1
d) ( x - 5 )4 =( x - 5 )6
=> (x-5)6:(x-5)4=1
=> (x-5)2=1
=> x-5=1
=> x=6
a) 57 . 53 : 510 = 510 : 510 = 1
b) 24 : 23 . 27 = 2 . 27 = 28
c) 93 : 33 . 272 = ( 32 ) 3 : 33 . ( 33 ) 2 = 36 : 33 . 36 = 33 . 36 = 39
d) 25 . 13 - 25 . 5 = 25 . ( 13 - 5 ) = 25 . 8 = 25 . 23 = 28
e) \(\frac{4^6.8^3}{4^8}=\frac{\left(2^2\right)^6.\left(2^3\right)^3}{\left(2^2\right)^8}=\frac{2^{12}.2^9}{2^{16}}=\frac{2^{21}}{2^{16}}=2^5\)
1/ 3(x - 2) = 9 => x - 2 = 3 => x = 5
2/ 3(x - 36) = 216 => x - 36 = 72 => x = 108
3/ (x - 3)3 = 33 => x - 3 = 3 => x = 6
4/ 2x = 32 => 2x = 25 => x = 5
5/ 3x - 16 = 2.74 : 73 = 14 => 3x = 30 => x = 10
6/ (6x - 39) : 3 = 201 => 6x - 39 = 603 => 6x = 642 => x = 107
7/ (3x - 15)2 = 81 => (3x - 15)2 = 92 => 3x - 15 = 9 => 3x = 24 => x = 8
8/ 3(x + 4) = 105 => x + 4 = 35 => x = 31
9/ 12x - 43 = 4.84 : 83 = 32 => 12x = 32 : 64 => 12x = 1/2 => x = 1/24
10/ 41 - (2x - 5) = 680 => 2x - 5 = -639 => 2x = -634 => x = - 317
b.\(3^{x+2}\)+4.\(3^{x+1}\)=7.\(3^6\)
\(3^2\).\(3^x\)+4.3.\(3^x\)=7.\(3^6\)
9.\(3^x\)+12.\(3^x\)=7.\(3^6\)
\(3^x\)(9+12)=7.\(3^6\)
\(3^x\).21=7.\(3^6\)
\(3^x\)=7.\(3^6\):21
\(3^x\)=\(3^6\):3
\(3^x\)=\(3^5\)
x=5
\(\left(3.x-2^4\right).7^3=2.8^4\)
\(\Leftrightarrow\left(3.x-16\right).343=2.4096\)
\(\Leftrightarrow\left(3.x-16\right).343=8192\)
\(\Leftrightarrow3.x-16=8192:343\)
\(\Leftrightarrow3.x-16=\frac{8192}{343}\)
\(\Leftrightarrow3.x=\frac{8192}{343}+16\)
\(\Leftrightarrow3.x=\frac{13680}{343}\)
\(\Leftrightarrow x=\frac{13680}{343}:3\)
\(\Leftrightarrow x=\frac{4560}{343}\)
(3.x-2^4).7^3=2.8^4
(3.x-16).343=2.4096
(3.x-16).343=8192
3.x-16 =8192:343
3.x-16 =23,88
3.x =23+16
3.x =39
x =39:3
x=13