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\(b,2.3^x+3^x=27\)
\(\Leftrightarrow3^x.\left(2+1\right)=27\)
\(\Leftrightarrow3^x.3=27\)
\(\Leftrightarrow3^x=27:3\)
\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2\)
\(\Rightarrow x=2\)
\(3^x.81^{2x+1}=81\)
\(3^x.3^{4x+4}=3^4\)
\(3^{5x+4}=3^4\)
\(3^{5x}.3^4=3^4\)
\(\Rightarrow3^{5x}=1\)
\(3^{5x}=3^0\)
\(\Rightarrow5x=0\)
\(\Rightarrow x=0\)
Vậy \(x=0\)
\(4^x-25=89\)
\(4^x=89+25\)
\(4^x=114\)
\(4^x=2.57\)
Ta có: 2.57 không chia hết cho 4
Mà \(x\in N\)
\(\Rightarrow4^x\ne114\)
\(\Rightarrow\)x không có giá trị
Vậy x không có giá trị
b) Tham khảo bài bạn TAKASA
Tham khảo nhé~
\(a)3^x\cdot81^{2x+1}=81\\ 3^x\cdot\left(3^4\right)^{2x+1}=81\\ 3^x\cdot3^{8x+4}=3^4\\ 3^{9x+4}=3^4\\ \Leftrightarrow9x+4=4\\ \Leftrightarrow9x=0\\ \Rightarrow x=0\)
\(b)4^x-25=89\\ \Leftrightarrow4^x=64\\ \Leftrightarrow4^x=4^3\\ \Rightarrow x=3\)
a) \(625^4:25^7\)
\(=\left[25^2\right]^4:25^7\)
\(=25^8:25^7\)
\(=25\)
b)\(\left(100^5-89^5\right).\left(6^8-8^6\right).\left(8^2-4^3\right)\)
\(=\left(100^5-89^5\right).\left(6^8-8^6\right).\left[\left(2^3\right)^2-\left(2^2\right)^3\right]\)
\(=\left(100^5-89^5\right).\left(6^8-8^6\right).\left[2^6-2^6\right]\)
\(=\left(100^5-89^5\right).\left(6^8-8^6\right).0\)
\(=0\)
a) \(3^x=81\)
\(3^x=3^4\)
\(\Rightarrow x=4\)
b) \(2^x.16=128\)
\(2^x=128:16\)
\(2^x=8\)
\(2^x=2^3\)
\(\Rightarrow x=3\)
c) \(3^x:9=27\)
\(3^x=27.9\)
\(3^x=243\)
\(3^x=3^5\)
\(\Rightarrow x=5\)
d) \(x^4=x\)
\(\Rightarrow x=0\)hoac \(\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
e) \(\left(2x+1\right)^3=27\)
\(\left(2x+1\right)^3=3^3\)
\(\Rightarrow2x+1=3\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=2\)
f) \(\left(x-2\right)^2=\left(x-2\right)^4\)
\(\left(x-2\right)^2-\left(x-2\right)^4=0\)
\(\left(x-2\right)^2-\left(x-2\right)^2.\left(x-2\right)^2=0\)
\(\left(x-2\right)^2\left[1-\left(x-2\right)^2\right]=0\)
\(\left(x-2\right)^2\left(1-x+2\right)\left(1+x-2\right)=0\)
\(\Rightarrow\left(x-2\right)^2=0\)hoac \(\orbr{\begin{cases}3-x=0\\x-1=0\end{cases}}\)
\(\Rightarrow x-2=0\)hoac \(\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
\(\Rightarrow x=2\)hoac \(\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
a) \(3^x=81\Leftrightarrow3^x=3^4\Rightarrow x=4\)
b)\(2^x\times16=128\Leftrightarrow2^x=8\Leftrightarrow2^x=2^3\Rightarrow x=3\)
c) \(3^x\div9=27\Leftrightarrow3^x\div3^2=3^3\Rightarrow x=5\)
d) \(x^4=x\Leftrightarrow x=1\)
e) \(\left(2x+1\right)^3=27\Leftrightarrow\left(2x+1\right)^3=3^3\Rightarrow2x+1=3 \)
\(\Rightarrow2x=3+1\Leftrightarrow2x=4\Rightarrow x=2\)
F)
a) 3x = 81 b) 2x . 16 = 128 c) 3x : 9 = 27 d) x4 = x
3x = 34 2x = 128 : 16 3x = 27 : 9 => x = 1
=> x = 4 2x = 8 3x = 3 Vậy x= 1
Vậy x = 4 x = 4 => x = 1
Vậy x = 4 Vậy x = 1
e) ( 2x + 1 )3 = 27
( 2x + 1 )3 = 33
=> 2x + 1 = 3
2x = 3 - 1
2x = 2
x = 1
Vậy x = 1
a, 3x=81 b, 2x*16=128 c, 3x:9=27 d, x4=x
=> 3x=34 => 2x=128:16 => 3x=27.9 => x=0 hoặc x=1
=> x=4 => 2x=8 => 3x=243
=> x=4 => 3x=35
=> x=5
e, (2x+1)3=27 f, (x-2)2=(x-2)4
=> (2x+1)3=33 +, TH1: x-2=1 => (x-2)2=(x-2)4=1 => x-2=x-2=1 => x=3
=> 2x+1=3 +, TH2: x-2=0 => (x-2)2=(x-2)4=0 => x-2=x-2=0 => x=2
=> 2x=2
=> x=2:2
=> x=1
g, 25 <= 5x < 625
=> 52 <= 5x < 54
=> x={2;3}
a) 3x.812x+1 = 81
3x.(34)2x+1 = 81
3x.38x+4 = 81
3x+8x+4 = 81 = 34
=> x + 8x + 4 = 4
9x + 4 = 4
9x = 0
x = 0
b) 2.3x+3x = 27
3x.(2+1) = 27
3x.3 = 27
3x = 9 = 32
=> x = 2
c) 4x -25 = 89
4x = 114
=>...
( câu c bn thử tìm xem có 4 mũ bao nhiêu = 114 ko nha! câu này mk ko tìm giúp bn đk)
3x.812x + 1 = 81
3x.38x + 4 = 81
39x + 4 = 81
9x + 4 = 4
9x = 0
x = 0