tìm x biết
2x.(22)2=(23)2
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\(2x-10,01=19,01-3\\ \Rightarrow2x-10,01=16,01\\ \Rightarrow2x=16,01+10,01\\ \Leftrightarrow2x=26,02\\ \Leftrightarrow x=26,02:2=13,01\)
2x-10,01=19,01-3
=> 2x-10,01= 16,01
=> 2x= 16,01+10,01
=>2x= 26,02
=> x= 26,02: 2= 13,01
a) Đặt: \(A=1+2^2+2^3+...+2^{10}\)
\(\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)\)
\(\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}\)
\(\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)\)
\(\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045\)
Vậy: \(1+2^2+2^3+...+2^{10}=2045\)
b)
a] \(60-3\left(x-1\right)=2^3\cdot3\)
\(\Rightarrow60-3\left(x-1\right)=24\)
\(\Rightarrow3\left(x-1\right)=36\)
\(\Rightarrow x-1=12\)
\(\Rightarrow x=13\)
b] \(\left(3x-2\right)^3=2\cdot2^5\)
\(\Rightarrow\left(3x-2\right)^3=2^6\)
\(\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3\)
\(\Rightarrow3x-2=2^2\)
\(\Rightarrow3x=6\)
\(x=2\)
c] \(5^{x+1}-5^x=500\)
\(\Rightarrow5^x\left(5-1\right)=500\)
\(\Rightarrow5^x\cdot4=500\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
d] \(x^2=x^4\)
\(\Rightarrow x=x^2\)
\(\Rightarrow x-x^2=0\)
\(\Rightarrow x\left(1-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
a: =>2x^3=58-4=54
=>x^3=27
=>x=3
b; =>(5-x)^5=2^5
=>5-x=2
=>x=3
c: =>(5x-6)^3=4^3
=>5x-6=4
=>5x=10
=>x=2
d: (3x)^3=(2x+1)^3
=>3x=2x+1
=>x=1
1=>2x3=54
=>x3=27 =>x=3
2=>(5-x)5=25
=>5-x=2
=>x=3
3=>(5x-6)3=43
=>5x-6=4
=>5x=10=>x=2
4=>3x=2x+1
=>x=1
\(PT\Leftrightarrow x^2+x\left(m^2-4m+4\right)+4=0\\ \Leftrightarrow x^2+x\left(m-2\right)^2+4=0\)
PT có 2 nghiệm pb \(\Leftrightarrow\left(m-2\right)^4-16>0\Leftrightarrow\left(m-2\right)^4>16\Leftrightarrow\left[{}\begin{matrix}x< 0\\x>4\end{matrix}\right.\)
1.Số tiền phải trả mua đt sai khi giảm giá là:
\(\dfrac{5000000\times\left(100-20\right)}{100}=4000000\left(đ\right)\)
2.\(16dm=160cm\)
\(\dfrac{x}{y}=\dfrac{5}{160}=0,03\)
3.\(2x+9=5\)
\(2x=5-9\)
\(2x=-4\)
\(x=-\dfrac{4}{2}=-2\)
1)
Số tiền được giảm:
\(\text{5000000}\times20\%=1000000\left(đông\right)\)
Giá tiền sau khi giảm :
\(5000000-1000000=4000000\left(đồng\right)\)
2)
16dm = 160 cm
Tỉ số % của x và y là:
\(5:160=\dfrac{5}{160}=\dfrac{1}{32}=0,03\)
Tìm x:
\(2x+9=5\)
\(2x=5-9\)
\(2x=-4\)
\(x=-4:2\)
\(x=-2\)
a) \(A=2+2^2+2^3+...+2^{2022}\)
\(2A=2.\left(2+2^2+2^3+...+2^{2022}\right)\)
\(2.A=2^2+2^3+2^4+...+2^{2023}\)
\(2A-A=\left(2^2+2^3+2^4+...+2^{2023}\right)-\left(2+2^2+2^3+...+2^{2022}\right)\)
\(A=2^{2023}-2\)
b) A + 2 = 2x
Hay \(\left(2^{2023}-2\right)+2=2^x\)
\(2^{2023}-2+2=2^x\)
\(2^{2023}=2^x\)
\(\Rightarrow x=2023\)
a, A = 21 + 22 + 23 + ...+ 22022
2A = 22 + 23 +...+ 22022 + 22023
2A - A = 22023 - 21
A = 22023 - 2
b, A + 2 = 2\(^x\) ⇒ 22023 - 2 + 2 = 2\(x\)
22023 = 2\(^x\)
2023 = \(x\)
2x*(22)2=(23)2
=>2x*24=26
=>2x=26/24
=>2x=26-4
=>2x=22
=>x=2
2x . (22)4 = (23)2
= 2x . 16 = 64
2x = 64 : 16
22 = 4
22 = 22
Suy ra : x = 2