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4. ( x - 250 ) : 6 = 64 - 12
( x- 250 ) : 6 = 52
x - 250 = 312
x = 562
5. 10x = 1030
=> x = 103
6. 30x = 120
x = 4
7. \(x=2023\)
\(8.165-\left(35:x+3\right).19=13\)
\(\left(35:x+3\right).19=152\)
\(35:x+3=8\)
\(35:x=5\)
\(x=7\)
4) \(\left(x-250\right)\div6=4^3-2^2\times3\)
\(\left(x-250\right)\div6=64-4\times3\)
\(\left(x-250\right)\div6=64-12=52\)
\(x-250=52\times6=312\)
\(x=312+250\)
\(x=562\)
5) \(2x+3x+5x=1030\)
\(x\left(2+3+5\right)=1030\)
\(10x=1030\)
\(x=1030\div10\)
\(x=103\)
6) \(15x-35x+50x=120\)
\(x\left(15-35+50\right)=120\)
\(30x=120\)
\(x=120\div30\)
\(x=4\)
7) \(\dfrac{1}{2}x+\dfrac{1}{6}x+\dfrac{1}{3}x=2023\)
\(x\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\right)=2023\)
\(x\times1=2023\)
\(x=2023\)
8) \(165-\left(35\div x+3\right)\times19=13\)
\(\left(35\div x+3\right)\times19=165-13\)
\(\left(35\div x+3\right)\times19=152\)
\(35\div x+3=152\div19=8\)
\(35\div x=8-3=5\)
\(x=35\div5\)
\(x=7\)
(2x2 + 1)(x-3)=0
\(\Rightarrow\orbr{\begin{cases}2x^2+1=0\\x-3=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x^2=-1\Rightarrow x^2=-\frac{1}{2}\left(vl\right)\\x=3\end{cases}}\)
Vậy x=3
48-(15-x)5=48
(15-x)5=48-48
(15-x)5=0
=> 15-x =0
x =15-0
x =15
Vậy x=15
\(2^{x+1}-1=63\\ 2^{x+1}=64\\ 2^{x+1}=2^6\\ =>X+1=6\\ =>x=5\)
\(\left(X-3\right)\cdot4^5=4^8\\ X-3=64\\ =>X=67\)
3 x (2x-1)2=48
=> (2x-1)2=48:3
=>(2x-1)2=16
Mà: 42=16 ; (-4)2=16
=> (2x-1)2 =42 hoặc (2x-1)2= (-4)2
=> 2x-1=4 hoặc 2x-1= -4
=> x= 2,5 hoặc x= -2,5
3 x ( 2x - 1 )2 = 48
=> ( 2x - 1 )2 = 48 : 3
=> ( 2x - 1 )2 = 16
=> ( 2x - 1 )2 = 42
=> 2x - 1 = 4 hoặc 2x - 1 = -4
+) 2x - 1 = 4
=> 2x = 5
=> x = 5/2
+) 2x - 1 = -4
=> 2x = -3
=> x = -3/2
Vậy x = 5/2 hoặc x = -3/2
1e) Để \(\frac{2x-1}{x-3}\) nguyên thì \(2x-1⋮x-3\)
\(\Leftrightarrow2x-6+5⋮x-3\)
\(\Leftrightarrow2\left(x-3\right)+5⋮x-3\)
Do \(2\left(x-3\right)⋮x-3\) \(\Rightarrow5⋮x-3\)
\(\Rightarrow x-3\in\left\{-5;-1;1;5\right\}\)
\(\Leftrightarrow x\in\left\{-2;2;4;8\right\}\)
Vậy:...................
a) \(2^x=8.64=2^3.2^6=2^9\Rightarrow x=9\)
b) \(3.2^x=48\Rightarrow2^x=16=2^4\Rightarrow x=4\)
\(a,2^{x+1}=32\\ 2^{x+1}=2^5\\ x+1=5\\ x=4\\ b,2^{2x}+2^{2x+1}=48\\ 2^{2x}+2\cdot2^{2x}=48\\ 3\cdot2^{2x}=48\\ 2^{2x}=16\\ 2^{2x}=2^4\\ 2x=4\\ x=2\)
\(c,3^x+5\cdot3^{x+1}=144\\ 3^x+15\cdot3^x=144\\ 16\cdot3^x=144\\ 3^x=9\\ 3^x=3^2\\ x=2\\ d,3^{x+5}=9^{x+1}\\ 3^{x+5}=3^{2x+2}\\ x+5=2x+2\\ x=3\)
\(2^{2x}+2^{2x+1}=48\)
\(2^{2x}+2^{2x}.2=48\)
\(2^{2x}.\left(1+2\right)=48\)
\(2^{2x}.3=48\)
\(2^{2x}=48:3\)
\(2^{2x}=16\)
\(2^{2x}=2^4\)
\(\Rightarrow2x=4\)
\(x=4:2\)
\(x=2\)
\(2^{x+3}-5.2^x=384\)
\(2^x.2^3-5.2^x=384\)
\(8.2^x-5.2^x=384\)
\(3.2^x=384\)
\(2^x=128\)
\(2^x=2^7\)
x=7
\(2^x+2^x.2=48\)
\(3.2^x=48\)
\(2^x=16\)
\(2^x=2^4\)
\(x=4\)