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\(\frac{86}{\left[2.\left(2x-1\right)^2-7\right]}+4^2=2.3^2\Leftrightarrow\frac{86}{\left[2.\left(2x-1\right)^2-7\right]}=2.9-4^2=2\)
\(\frac{86}{2}=\left[2.\left(2x-1\right)^2-7\right]=2.\left(2x-1\right)^2-7\)
\(43=2.\left(2x-1\right)^2-7\Leftrightarrow2.\left(2x-1\right)^2=43+7=50\)
\(\left(2x-1\right)^2=\frac{50}{2}=25=5^2\Rightarrow!2x-1!=5\)
\(\orbr{\begin{cases}2x-1=-5\\2x-1=5\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=-4\\2x=6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=3\end{cases}}}}\)
86 : [2 . (2x - 1)2 - 7] +42=2.32
86 : [2.(2x-1)2-7] + 16 = 2.9
86 : [2.(2x-1)2-7] +16 = 18
86 : [2.(2x-1)2-7]=18-16
86 : [2.(2x-1)2-7]=2
2.(2x-1)2-7=86:2
2.(2x-1)2-7=43
2.(2x-1)2=43+7
2.(2x-1)2=50
(2x-1)2=50:2
(2x-1)2=25
(2x-1)2=52
=>2x-1=5
2x=5+1
2x=6
x=6:2
x=3
\(7\left(x-9\right)=35\Leftrightarrow x-9=5\Leftrightarrow x=14\)
Câu 2: \(2^x=2^2\cdot2\Leftrightarrow2^x=2^3\Leftrightarrow x=3\)
Câu 3: \(2\cdot3^{x-1}=54\Leftrightarrow3^{x-1}=27\Leftrightarrow3^{x-1}=3^3\Leftrightarrow x-1=3\Leftrightarrow x=4\)
Câu 4: \(42-\left(2x+32\right)+12:2=6\)
\(\Leftrightarrow42-2x-32+6=6\)
\(\Leftrightarrow-2x=6-6+32-42=-10\)
\(\Leftrightarrow x=5\)
Cau 1: 7.(x-9)=35
x-9=35:7
x-9=5
x=5+9
x=14
Cau2: 2:2^x=2^2.2
2:2^x=8
2^x=8.2
2^x=16
=> x=4
a) \(\left(\left|x\right|+3\right):5-3=12\Leftrightarrow\left|x\right|+3=45\Leftrightarrow\orbr{\begin{cases}x=42\\x=-42\end{cases}}\)
b) \(86:\left[2\left(2x-1\right)^2-7\right]+4^2=2\cdot3^2\Leftrightarrow2\left(2x-1\right)^2-7=43\Leftrightarrow\left(2x-1\right)^2=25\Leftrightarrow\orbr{\begin{cases}2x-1=-5\\2x-1=5\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)
a) \(\left(\left|x\right|+3\right)\div5-3=12\)
\(\left(\left|x\right|+3\right)\div5=12+3\)
\(\left(\left|x\right|+3\right)\div5=15\)
\(\left|x\right|+3=15.5\)
\(\left|x\right|+3=75\)
\(\left|x\right|=75-3\)
\(\left|x\right|=72\)
\(\Rightarrow\orbr{\begin{cases}x=72\\x=-72\end{cases}}\)
Vậy \(x\in\left\{72;-72\right\}\)
b) \(86\div\left[2,\left(2x-1\right)^2-7\right]+4^2=2.3^2\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]+16=18\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]=18-16\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]=2\)
\(2.\left(2x-1\right)^2-7=86\div2\)
\(2.\left(2x-1\right)^2-7=43\)
\(2.\left(2x-1\right)^2=43+7\)
\(2.\left(2x-1\right)^2=50\)
\(\left(2x-1\right)^2=50\div2\)
\(\left(2x-1\right)^2=25\)
\(\left(2x-1\right)^2=5^2\)
\(\Rightarrow2x-1=5\)
\(2x=5+1\)
\(2x=6\)
\(x=6\div2\)
\(x=3\)
\(\left(2x+1\right)^3=125\\ \Rightarrow\left(2x+1\right)^3=5^3\\ \Rightarrow2x+1=5\\ \Rightarrow2x=4\\ \Rightarrow x=2.\\ b,\left(2x-1\right)^4=16\\ \Rightarrow\left(2x-1\right)^4=2^4\\ \Rightarrow2x-1=2\\ \Rightarrow2x=3\\ \Rightarrow x=\dfrac{3}{2}.\\ c,6.3^x-2.3^x=36\\ \Rightarrow3^x.\left(6-2\right)=36\\ \Rightarrow3^x.4=36\\ \Rightarrow3^x=9\\ \Rightarrow3^x=3^2\\ \Rightarrow x=2.\\ d,2^{x+1}-2^x=32\\ \Rightarrow2^x.\left(2-1\right)=32\\ \Rightarrow2^x=2^5\\ \Rightarrow x=5.\)