( x - 3)2 = 64/81
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\(9^7.81:9^5=9^7.9^2:9^5=9^{7+2-5}=9^4\\ x^{12}:x.x^8=x^{12-1+8}=x^{19}\\ 16.2^4:8=2^4.2^4:2^3=2^{4+4-3}=2^5\\ 64.4^5:16=4^3.4^5:4^2=4^{3+5-2}=4^6\\ 3^{12}.3:3^8=3^{12+1-8}=3^5\\ 7^9.7^{12}:2015^0=7^{9+12}:1=7^{19}\)
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a, 410. 230=220.230=250
b,925.274.813= 350.312.312=374
Tương tự các câu khác....
a, 410.230 = (22)10.230 = 220.230 = 250
b, 925.274.813 = (32)25.(33)4.(34)3 = 350.312.312 = 374
c, 2550.1255 = (52)50.(53)5 = 5100.515 = 5115
d, 643.48.164 = (26)3.(22)8.(24)4 = 218.216.216 = 250
e, 38 : 36 = 32
210 : 83 = 210 : (23)3 = 210 : 29 = 2
127 : 67 = (12 : 6)7 = 27
@Dương Tuyết Mai
![](https://rs.olm.vn/images/avt/0.png?1311)
4x = 64 = 43 => x = 3
2x = 16 = 24 => x = 4
3x = 81 = 34 => x = 4
![](https://rs.olm.vn/images/avt/0.png?1311)
a, 2x-1 = 64
=> 2x-1 = 26
=> x - 1 = 6
=> x = 6 + 1
=> x = 7
b, 32x-10 = 81
=> 32x-10 = 34
=> 2x - 10 = 4
=> 2x = 14
=> x = 7
c, 22x+3 = 1024
=> 22x+3 = 210
=> 2x + 3 = 10
=> 2x = 7
=> x = \(\frac{7}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^x=32\)
\(\Leftrightarrow2^x=2^5\)
\(\Leftrightarrow x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a,
\(\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)
\(\dfrac{1}{4}:x=\dfrac{2}{5}-\dfrac{3}{4}\\ \)
\(\dfrac{1}{4}:x=\dfrac{8-15}{20}\)
\(\dfrac{1}{4}:x=\dfrac{-7}{20}\)
x = \(\dfrac{1}{4}:\dfrac{-7}{20}\)
\(x=\dfrac{-5}{7}\)
b,
( 3x + 1)^3 = 64
(3x + 1)^3 = 4^3
(3x + 1) = 4
3x = 4 - 1
3x = 3
x = 3 : 3
x = 1
c,
( 2x - 3)^4 = 81
( 2x - 3) ^4 = 3^4
(2x - 3) = 3
2x = 3 + 3
2x = 6
x = 6: 2
x = 3
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(2^{x^2-1}=256\)
=>\(2^{x^2-1}=2^8\)
=>\(x^2-1=8\)
=>\(x^2=9\)
=>\(x\in\left\{3;-3\right\}\)
b: \(3^{x^2+3x}=81\)
=>\(3^{x^2+3x}=3^4\)
=>\(x^2+3x=4\)
=>\(x^2+3x-4=0\)
=>(x+4)(x-1)=0
=>\(\left[{}\begin{matrix}x+4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=1\end{matrix}\right.\)
c: \(2^{x^2-5x}=64\)
=>\(2^{x^2-5x}=2^6\)
=>\(x^2-5x=6\)
=>\(x^2-5x-6=0\)
=>(x-6)(x+1)=0
=>\(\left[{}\begin{matrix}x-6=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-1\end{matrix}\right.\)
d: \(\left(\dfrac{1}{3}\right)^x=243\)
=>\(\left(\dfrac{1}{3}\right)^x=3^5=\left(\dfrac{1}{3}\right)^{-5}\)
=>x=-5
e: \(\left(\dfrac{1}{3}\right)^{x+5}=3^{2x+1}\)
=>\(3^{-x-5}=3^{2x+1}\)
=>-x-5=2x+1
=>-3x=6
=>x=-2
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 10:
a) (1/3)n = 1/81
=> (1/3)n = (1/3)4
=> n = 4
b) -512/343 = (-8/7)n
=> (-8/7)3 = (-8/7)n
=> 3 = n (hay n = 3)
c) (-3/4)n = 81/256
=> (-3/4)n = (-3/4)4
=> n = 4
d) 64/(-2)n = (-2)3
=> 64/(-2)n = -8
=> (-2)n = -8
=> (-2)n = (-2)3
=> n = 3
Bài 11: (không có y để tìm nhé)
a) (0,4x - 1,3)2 = 5,29
=> (0,4x - 1,3)2 = (2,3)2
=> 0,4x - 1,3 = 2,3
=> 0,4x = 3,6
=> x = 9
b) (3/5 - 2/3x)3 = -64/125
=> (3/5 - 2/3x)3 = (-4/5)3
=> 3/5 - 2/3x = -4/5
=> 2/3x = 7/5
=> x = 21/10
\(\left(x-3\right)^2=\frac{64}{81}\)
\(\Rightarrow\left(x-3\right)^2=\left(\frac{8}{9}\right)^2\)
\(\Rightarrow\orbr{\begin{cases}x-3=\frac{8}{9}\\x-3=\frac{-8}{9}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{8}{9}+3\\x=\frac{-8}{9}+3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{35}{9}\\x=\frac{19}{9}\end{cases}}\)