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| x - 1 | + | x + 3 | = 3 ( * )
xét : x - 1 = 0 => x = 1
x + 3 = 0 => x = -3
x - 1 < 0 => x < 1
x + 3 < 0 => x < -3
x - 1 > 0 => x > 1
x + 3 > 0 => x > -3
Lập bảng xét dấu,ta có :
x -3 1
x+3 - 0 + | +
x-1 - | - 0 +
nếu x < -3 thì * <=> : ( 1 - x ) + ( -3 - x ) = 3
1 - x + ( -3 ) - x = 3
-2x = 5
x = -5/2 ( loại )
nếu -3 \(\le\)x < 1 thì * <=> : ( 1 - x ) + ( x + 3 ) = 3
1 - x + x + 3 = 3
0x = -1 ( ko có GT x thỏa mãn )
nếu x \(\ge\)1 thì * <=> : ( x -1 ) + ( x + 3 ) = 3
x - 1 + x + 3 = 3
2x = 1
x = 1/2 ( ko có GT x thỏa mãn )
Vậy ko có GT x nào thỏa mãn bài trên.
a) 25 < 5n:5 < 625
52 < 5n:5 < 54
2 < n:5 < 4
=> n : 5 = 3
=> n = 15
b) 34 < \(\frac{1}{9}.27^n\)< 310
34 < \(\frac{27^n}{9}\)< 310
34 < 33n-2 < 310
=> 3n - 2 \(\in\) { 5 ; 6 ; 7 ; 8 ; 9 }
Nếu 3n - 2 = 5 thì n = 7/3 ( loại )
Nếu 3n - 2 = 6 thì n = 8/3 ( loại )
Nếu 3n - 2 = 7 thì n = 3 ( thỏa mãn )
Nếu 3n - 2 = 8 thì n = 10/3 ( loại )
Nếu 3n - 2 = 9 thì n = 11/3 ( loại )
Vậy n = 3
![](https://rs.olm.vn/images/avt/0.png?1311)
\(27^5.3^x=9^{10}\)
\(\Rightarrow\left(3^3\right)^5.3^x=\left(3^2\right)^{10}\)
\(\Rightarrow3^{15}.3^x=3^{20}\)
\(\Rightarrow3^x=3^{20}:3^{15}\)
\(\Rightarrow3^x=3^5\)
\(\Rightarrow x=5\)
Vậy \(x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{a, 3(x+1)+4x=10}\)
\(\Rightarrow3x+3+4x=10\)
\(\Rightarrow7x+3=10\)
\(\Rightarrow7x=10-3=7\)
\(\Rightarrow x=1\)
c, x+1/10+x+2/9=x+3/8+x+4/7
=> (x+1/10 +1) +(x+2/9 +1)= ( x+3/8 +1) +(x+4/7 +1)
=> x+11/10 + x+11/9 = x+11/8 + x+11/7
...............
a) \(3\left(x+1\right)+4x=10\)
\(\Rightarrow3x+3+4x=10\)
\(\Rightarrow3x+4x=10-3\)
\(\Rightarrow7x=7\)
\(\Rightarrow x=7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 4:
\(a,2^{30}=\left(2^3\right)^{10}=8^{10};3^{20}=\left(3^2\right)^{10}=9^{10}\\ Vì:8^{10}< 9^{10}\left(Vì:8< 9\right)\Rightarrow2^{30}< 3^{20}\\ b,9^{10}.27^5=\left(3^2\right)^{10}.\left(3^3\right)^5=3^{20}.3^{15}=3^{35}\\ 243^7=\left(3^5\right)^7=3^{35}\\ Vì:3^{35}=3^{35}\Rightarrow243^7=9^{10}.27^5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(27^5.3^x=9^{10}\)
\(\left(3^3\right)^5.3^x=\left(3^2\right)^{10}\)
\(3^{15}.3^x=3^{20}\)
\(\Rightarrow3^x=3^{20}-3^{15}\)
\(\Rightarrow3^x=3^5\)
\(\Rightarrow x=5\)
Vậy x= 5
k mik nha
\(\Leftrightarrow3^{15}.3^x=3^{20}\)
\(\Leftrightarrow3^{15+x}=3^{20}\)
\(\Leftrightarrow15+x=20\)
\(\Leftrightarrow x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 6 :
a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)
b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)
c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)
d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)
Bài 7 :
a) \(3^x+3^{x+2}=9^{17}+27^{12}\)
\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)
\(\Rightarrow10.3^x=3^{34}+3^{36}\)
\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)
\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)
b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)
\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)
\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)
c) Bài C bạn xem lại đề
d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)
\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)
\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)
\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)
\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)
\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1, 27x.9x=927:81
(33)x.(32)X=(32)27:34
33X.32X=354:34
33X+2X=350
35X=350
Suy ra :5x=50
x=10
![](https://rs.olm.vn/images/avt/0.png?1311)
1) Tìm số nguyên x, biết :
a) 3x = 94/ 273
3x = 1/3
3x = 3-1
=> x = -1
b) 3x = 98 / 273 . 812
3x = 37.38
3x = 315
=> x = 15
c) 2x - 3 / 410 = 83
2x - 3 = 83.410
2x - 3 = 226
=> x - 3 = 26
=> x = 29
d) 22x - 3 / 410 = 83 . 165
22x - 3 / 410 = 269
22x - 3 = 269 . 410
22x - 3 = 289
=> 2x - 3 = 89
2x = 91
x = 91/2
e) 35 / 3x = 310
3x = 35 : 310
3x = 3-5
=> x = -5
27^5.3^x=9^10
3^x=9^10:27^5
3^x=3^5
=> x=5
275.3x=910
=>315.3x=330
=>3x=330:315
=>3x=315
=>x=15