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a)\(3^{x-2}+3^x=810\)
\(\Leftrightarrow3^x\left(3^{-2}+1\right)=810\)
\(\Leftrightarrow3^x\cdot\frac{10}{9}=810\)
\(\Leftrightarrow3^x=729\)
\(\Leftrightarrow3^x=3^6\)
\(\Leftrightarrow x=6\)
b)402240223.(x2-1)=804480443
\(\Leftrightarrow x^2-1=80448044^3:40224022^3\)
\(\Leftrightarrow x^2-1=\left(\frac{80448044}{40224022}\right)^3\)
\(\Leftrightarrow x^2-1=2^3\)
\(\Leftrightarrow x^2=9\)
\(\Leftrightarrow x=\pm3\)
a) \(6x-36=5^{12}:5^{10}-2012^0\)
\(6x-36=5^2-2012^0\)
\(6x-36=25-1\)
\(6x-36=24\)
\(6x\) \(=24+36\)
\(6x\) \(=60\)
\(x=60:6\)
\(x=10\)
Vậy \(x=10\)
b) \(2x-125=-65\)
\(2x\) \(=\left(-65\right)+125\)
\(2x\) \(=60\)
\(x=60:2\)
\(x=30\)
Vậy \(x=30\)
c) \(2012-120\left(4x+1\right)=932\)
\(120\left(4x+1\right)=2012-932\)
\(120\left(4x+1\right)=1080\)
\(4x+1=1080:120\)
\(4x+1=9\)
\(4x\) \(=9-1\)
\(4x\) \(=8\)
\(x=8:4\)
\(x=2\)
Vậy \(x=2\)
a) 6x - 36 = 512 : 510 - 20120
6x - 36 = 52 - 20120
6x - 36 = 25 - 1
6x - 36 = 24
6x = 24 + 36
6x = 60
x = 60 : 6
x = 10
Vậy x = 10
b) 2x - 125 = -65
2x = (-65) + 125
2x = 60
x = 60 : 2
x = 30
Vậy x = 30
c) 2012 - 120(4x + 1) = 932
120(4x + 1) = 2012 - 932
120(4x + 1) = 1080
4x + 1 = 1080 : 120
4x + 1 = 9
4x = 9 - 1
4x = 8
x = 8 : 4
x = 2
Vậy x = 2.
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⇔(2 x ) 2+2.2 x .1+1 2=0 ... c ,(3 x −4) 2−14(3 x −4)(6+3 x )+49(3 x +6)=16 ... ⇔9 x 2−24 x +16−126 x 2−252 x +168 x +336+147 x +294=16.
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c) x.(1+2+3+4+...+100)=0
x.5050=0
x=0:5050=0
Vậy x=0
d) x.(1+2+3+4+5+...+100)=5050
x.5050=5050
x=1
Vậy x=1
e) x+1+x+2+x+3+x+4+...+x+100=5050
(x+x+x+x+...+x)+(1+2+3+4+...+100)=5050
100 số hạng x
x.100+5050=5050
x.100=0
x=0
Vậy x=0
\(2x+4x+6x+........+98x+100x=51.10^2\)
\(\Rightarrow x\left(2+4+6+.........+98+100\right)=51.100\)
\(\Rightarrow x.2550=5100\)
\(\Rightarrow x=5100:2550\)
\(\Rightarrow x=2\)
Vậy x = 2
\(2x+4x+6x+...+100x=51.10^2\)
\(\Rightarrow x\left(2+4+...+100\right)=5100\)
\(\Rightarrow x\left(\frac{\left[\left(100-2\right):2+1\right].\left(100+2\right)}{2}\right)=5100\)
\(\Rightarrow x\left(\frac{50.102}{2}\right)=5100\)
\(\Rightarrow\frac{5100x}{2}=5100\)
\(\Rightarrow5100x=5100.2\)
\(\Rightarrow x=2\)