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a: \(\Leftrightarrow\left[\left(3x+14\right):4-3\right]:2=1\)
=>(3x+14):4-3=2
=>(3x+14):4=5
=>3x+14=20
=>3x=6
hay x=2
b: \(\Leftrightarrow\left[\left(x:4+17\right):10+3\cdot16\right]:10=5\)
\(\Leftrightarrow\left(x:4+17\right):10=50-48=2\)
=>x:4+17=20
=>x:4=3
hay x=12
c: \(\Leftrightarrow2\cdot15^2+\left[2\cdot125-\left(2x+4\right)\cdot5\right]:19=453\)
\(\Leftrightarrow250-\left(2x+4\right)\cdot5=\left(453-450\right)\cdot19=57\)
=>5(2x+4)=197
=>2x+4=197/5
=>2x=177/5
hay x=177/10
d: \(\Leftrightarrow\left(19x+50\right):14=5^2-4^2=9\)
=>19x+50=126
=>19x=76
hay x=4
e: \(\Leftrightarrow2\cdot3^x=10\cdot3^{12}+8\cdot3^{12}=18\cdot3^{12}\)
\(\Leftrightarrow3^x=3^2\cdot3^{12}=3^{14}\)
hay x=14
f: \(\Leftrightarrow3\left(x+2\right):7=30\)
=>3(x+2)=210
=>x+2=70
hay x=68
g: \(2480-1570+200-x+5=1010\)
=>1115-x=1010
hay x=105
a, 13.(x-9)=169
x-9 =169:13
x-9 =13
b, 230+[16+(x,-5)]=315.2\(^3\)
230+[16+(x,-5)]=2520
16+(x,-5)=2520-230
16+(x-5)=2290
x-5 =2290-16
x-5 =2274
x =2274+5
x =2279
c, 13x-3\(^2\)x=2003\(^1\)+1\(^{2016}\)
13x-9x=2004
(13-9)x=2004
4 . x=2004
x=2004:4
x=501
\(5^{x-1}=125\)
\(5^{x-1}=5^3\)
\(\Rightarrow x-1=3\)nên x = 4
c) \(5^{x+2}+5^x=650\)
\(\Leftrightarrow 5^x(5^2+1)=650\)
\(\Leftrightarrow 5^x.26=650\)
\(\Rightarrow 5^x=25=5^2\Rightarrow x=2\)
d) \(81^x=(-3)^7\)
Ta thấy \(81^x>0, \forall x\in\mathbb{R}\)
\((-3)^7<0\)
Do đó pt đã cho vô nghiệm.
Lời giải:
a) \((2x-1)^3=(2x-1)^4\)
\(\Leftrightarrow (2x-1)^4-(2x-1)^3=0\)
\(\Leftrightarrow (2x-1)^3[(2x-1)-1]=0\)
\(\Leftrightarrow (2x-1)^3(2x-2)=0\)
\(\Rightarrow \left[\begin{matrix} 2x-1=0\\ 2x-2=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{1}{2}\\ x=1\end{matrix}\right.\)
b) \(2017^{x+2}=(2018-5^3)^{x+2}\)
\(\Rightarrow \left[\begin{matrix} x+2=0(1)\\ 2017=2018-5^3(2)\end{matrix}\right.\)
(1)\(\Rightarrow x=-2\)
(2): hiển nhiên vô lý
Vậy pt có nghiệm $x=-2$
a, 5 . ( x - 6 ) - 415 = 15
5 . ( x -6 ) = 15 + 415
5 . ( x - 6 ) = 430
x-6 = 430 : 5
x - 6 = 86
x = 86 + 6
x = 92
b, ( 3 . x - 12 ) . 3 = \(3^3\)
3 . x - 12 = 27 : 3
3 . x - 12 = 9
3. x = 9 + 12
3 . x = 21
x = 21 : 3
x = 7
x, \(\left(5-x\right)^2\) . \(2^2\) = 64
\(\left(5-x\right)^2\) . 4 = 64
\(\left(5-x\right)^2\) = 64 : 4
\(\left(5-x\right)^2\) = 16
\(\left(5-x\right)^2\) = \(4^2\)
5 - x = 4
x = 5 -4
x =1
Tk mk nha
a) 5x + 5x+2 =650
5x ( 1 + 52)=650
5x . 26 = 650
5x = 650 : 26 = 25= 52
=> x = 2
b) (7x + 2)-1 = 3-2
\(\frac{1}{7x+2}=\frac{1}{3^2}\)
\(\Rightarrow7x+2=9\)
\(7x=9-2=7\)
\(x=\frac{7}{7}=1\)
cảm ơn bn nhiều