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Bài 1 :
\(2^x.8=512\)
\(2^x=512:8\)
\(2^x=64\)
\(2^x=2^6\)
\(\Rightarrow x=6\)
\(b,\left(2x+1\right)^3=125\)
\(\left(2x+1\right)^3=5^3\)
\(\Rightarrow2x+1=5\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=2\)
\(c,x^{20}=x\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
\(d,\left(x-3\right)^{10}=0\)
\(\Rightarrow x-3=0\)
\(\Rightarrow x=3\)
\(A=2^2+2^2+2^3+2^4+...+2^{2006}\)
\(2A=2^3+2^3+2^4+2^5+...+2^{2007}\)
\(2A-A=2^{2007}+2^3-\left(2^2+2^2\right)\)
\(A=2^{2007}+8-8\)
\(A=2^{2007}\)
\(\Rightarrow\text{ }2A=2^{2008}=2^{2\cdot1004}=\left(2^2\right)^{1004}=4^{1004}\)
\(\Rightarrow\text{ }x=1004\)
Đặt B=2^2+2^3....+2^2006
2B=2^3+2^4+....+2^2007
=>2B-B=(2^3+2^4+...+2^2007)-(2^2+2^3+....+2^2006)
B=2^2007-2^2
=>A=2^2007-2^2+2^2
A=2^2007
=>2A=2^2008
=>2A=4^1004
Vậy x=1004
1/
a. \(x^3-2=25\)
\(x^3=25+2\)
\(x^3=27\)
\(\Rightarrow x=3\)
b.\(\left(x-3\right)^2=25\)
\(\left(x-3\right)^2=5^2\)
\(\Rightarrow x-3=5\)
\(\Rightarrow x=8\)
1,a, x^3-2=25 b, (x-3)^2=25 c, x^3-x^2=55 d,[(8.x-12):4].3^7=3^10
x^3=27 (x-3)^2=5^2 không có giá trị x (8.x-12):4=3^3
x^3=3^3 x-3=5 8.x-12=108
x=3 x=8 8.x=120
x=15
2, a, \(7^6:7^4+3^4.3^2-3^7:3\) b, 1736-(21-16).32+6.7^2 c,56.17+17.44-4^3.5+6.(3^2-2)
=\(7^2+3^6-3^6\) =1736-5.32+6.49 =17.(56+44)-320+42
=\(49\) =1736-160+294 =17.10-278
=1736+134 =170-278
=1870 =-108
d, 3.10^2-[1200-(4^2-2.3)^3]
=300-[1200-(16-6)^3]
=300-(1200-10^3)
=300-(1200-1000)
=300-200
=100
\(5^x+5^{x+2}=650;5^x.26=650;5^x=25;x=2\)
\(2^x+2^{x+3}=144;2^x.9=144;2^x=16;x=4\)
\(3^{x-1}+5.3^{x-1}=162;3^{x-1}.6=162;3^{x-1}=27;x=4\)
\(\left(x-5\right)^4=\left(x-5\right)^6\)
\(\rightarrow x-5=0\&x-5=1\) hoặc x - 5 = - 1
\(x-5=1;x=6;x-5=0;x=5;x-5=-1;x=4\)
\(\left(2^2:4\right).2^n=4;2^n=2^2;n=2\)
13/ => 10 + 2x = 42 = 16
=> 2x = 6
=> x = 3
14/ => 52x : 53 - 50 = 75
=> 52x : 53 = 125 = 53
=> 52x = 56
=> 2x = 6
=> x = 3
15/ => (26 - 3x) : 5 = 4
=> 26 - 3x = 20
=> 3x = 6
=> x = 2
16/ => x - 17 = -25
=> x = -8
\(1)6^{x-3}=6^0\)
\(\Rightarrow x-3=0\)
\(x=3\)
\(2)17-x=20\)
\(x=-3\)
\(3)5^{x-2}=5^2\)
\(\Rightarrow x-2=2\)
\(x=4\)
\(4)579-3x=9.16\)
\(579-3x=144\)
\(3x=435\)
\(x=145\)
\(5)15-x=8+12\)
\(15-x=20\)
\(x=-5\)
\(6)4\left(3x-4\right)=20\)
\(3x-4=5\)
\(3x=9\)
\(x=3\)
\(7)3^{x+4}=3^5\)
\(\Rightarrow x+4=5\)
\(x=1\)
\(8)40-x=14+27\)
\(40-x=41\)
\(x=-1\)
\(9)12x-91=101\)
\(12x=192\)
\(x=16\)
\(10)5x-206=16.4\)
\(5x-206=64\)
\(5x=270\)
\(x=54\)
( 19x + 2 . 52 ) : 14 = ( 13 - 8 )2 - 42
( 19x + 2 .25 ) : 14 = 52 - 42
( 19x + 100 ) : 14 = 25 - 16
( 19x + 100 ) : 14 = 9
( 19x + 100 ) = 76
19x = -24
x ko tìm đk
B1. 2x + 3 + 22 = 72
=> 2x + 3 + 4 = 72
=> 2x + 3 = 72 - 4
=> 2x + 3 = 68
=> ko có gtri x
B2 : Ta có : A = 1 + 2 + 22 + 23 + 24 + 25 + 26 + ... + 22001 + 22002
= (1 + 2) + (22 + 23 + 24) + (25 + 26 + 27) + ... + (22000 + 22001 + 22002)
= 3 + 22.(1 + 2 + 22) + 25.(1 + 2 + 22 ) + ... + 22000 . (1 + 2 + 22)
= 3 + 22.7 + 25.7 + ... + 22000 . 7
= 3 + (22 + 25 + .... + 22000) . 7
=> Số dư của 7 là 3
\(2^{x+4}=2^2\cdot8\)
\(2^{x+4}=2^2\cdot2^3\)
\(2^{x+4}=2^5\)
\(\Rightarrow x+4=5\Rightarrow x=1\)
2^x+4 = 2^2 nhân 2^3
2^x+4=2^5
x+4=5
x = 5-4
x =1