8.2 mũ x=128
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a)125-3.(x+3)=65
3 .(x + 3) = 125 - 65
3. (x + 3) = 60
x + 3 = 60 : 3
x+3 = 20
x = 20-3
x=17
b) 8.2x = 128
2x = 128 : 8
2x = 16
2x = 24
=> x = 4
Bài 9:
a) Ta có: \(A=\left(2x+y\right)^2-\left(2x+y\right)\left(2x-y\right)+y\left(x-y\right)\)
\(=4x^2+4xy+y^2-4x^2+y^2-xy-y^2\)
\(=3xy-y^2\)
\(=3\cdot\left(-2\right)\cdot3-3^2=-18-9=-27\)
b) Ta có: \(B=\left(a-3b\right)^2-\left(a+3b\right)^2-\left(a-1\right)\left(b-2\right)\)
\(=a^2-6ab+9b^2-a^2-6ab-9b^2-ab+2a+b-2\)
\(=-13ab+2a+b-2\)
\(=-13\cdot\dfrac{1}{2}\cdot\left(-3\right)+2\cdot\dfrac{1}{2}+\left(-3\right)-2\)
\(=\dfrac{31}{2}\)
Bài 7:
a) \(498^2=\left(500-2\right)^2=250000-2000+4=248004\)
b) \(93\cdot107=100^2-7^2=10000-49=9951\)
c) \(163^2+74\cdot163+37^2=\left(163+37\right)^2=200^2=40000\)
d) \(1995^2-1994\cdot1996=1995^2-1995^2+1=1\)
e) \(9^8\cdot2^8-\left(18^4-1\right)\left(18^4+1\right)\)
\(=18^8-18^8+1=1\)
f) \(125^2-2\cdot125\cdot25+25^2=\left(125-25\right)^2=100^2=10000\)
`@` `\text {Ans}`
`\downarrow`
`32^x \div 16^x = 128`
`=> (2^5)^x \div (2^4)^x = 2^7`
`=> 2^(5x) \div 2^(4x) = 2^7`
`=> 2^(5x - 4x) = 2^7`
`=> 2^x = 2^7`
`=> x = 7`
Vậy, `x = 7.`
phần a chép thiếu r bn
b) (x-2)4 = (x-2)6
=> (x-2)4 - (x-2)6 = 0
(x-2)4.[1-(x-2)2 ] = 0
=> (x-2)4 = 0 => x -2 = 0 => x = 2
1- (x-2)2 = 0 => (x-2)2 = 1 => x - 2 = 1 => x = 3
x - 2 = -1 => x = 1
KL:...
16x<1284
<=> (24)x < (27)4
<=> 2 4x< 228
=> 4x < 28 => x < 7
Đáp số: x < 7
\(a,2^x.4=128\)
\(\Leftrightarrow2^x=128:4\)
\(\Leftrightarrow2^x=32\)
\(\Leftrightarrow2^x=2^5\)
\(\Rightarrow x=5\)
\(b,2^x=4.128\)
\(\Leftrightarrow2^x=2^2.2^7\)
\(\Leftrightarrow2^x=2^9\)
\(\Rightarrow x=9\)
\(c,3^x=3^3.3^5\)
\(\Leftrightarrow3^x=3^8\)
\(\Rightarrow x=8\)
\(d,2^x.\left(2^2\right)^3=\left(2^3\right)^2\)
\(\Leftrightarrow2^x.2^6=2^6\)
\(\Leftrightarrow2^x=2^6:2^6\)
\(\Leftrightarrow2^x=1\)
\(\Rightarrow x=0\)
\(4< 2^x< 128\Rightarrow2^2< 2^x< 2^7\) \(\Rightarrow2< x< 7\)
\(8\cdot2^x=128\)
\(\Rightarrow2^x=128:8=16\)
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
ti ck nha
8.2^4=128 nha
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