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a, 3.(2\(x\) + 4) + 198 = (-3)2.10
3.(2\(x\) + 4) + 198 = 90
3.(2\(x\) + 4) = 90 - 198
3.(2\(x\) + 4) = - 108
2\(x\) + 4 = -108 : 3
2\(x\) + 4 = -36
2\(x\) = - 36 - 4
2\(x\) = - 40
\(x\) = -40 : 2
\(x\) = - 20
b, 2.(\(x\) + 7) - 6 = 18
2.(\(x\) + 7) = 18 + 6
2.(\(x\) + 7) =24
\(x\) + 7 = 24 : 2
\(x\) + 7 = 12
\(x\) = 12 - 7
\(x\) = 5
\(a,2^{x+1}=32\\ 2^{x+1}=2^5\\ x+1=5\\ x=4\\ b,2^{2x}+2^{2x+1}=48\\ 2^{2x}+2\cdot2^{2x}=48\\ 3\cdot2^{2x}=48\\ 2^{2x}=16\\ 2^{2x}=2^4\\ 2x=4\\ x=2\)
\(c,3^x+5\cdot3^{x+1}=144\\ 3^x+15\cdot3^x=144\\ 16\cdot3^x=144\\ 3^x=9\\ 3^x=3^2\\ x=2\\ d,3^{x+5}=9^{x+1}\\ 3^{x+5}=3^{2x+2}\\ x+5=2x+2\\ x=3\)
Bài 1:
Ta có: \(4-2\left(x+1\right)=2\)
\(\Leftrightarrow2\left(x+1\right)=2\)
\(\Leftrightarrow x+1=1\)
hay x=0
Bài 2:
Ta có: \(\left|2x-3\right|-1=2\)
\(\Leftrightarrow\left|2x-3\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)
Câu 1: Ta có: \(B=3^{75}=\left(3^3\right)^{25}=27^{25}\)
\(C=2^{100}=\left(2^4\right)^{25}=16^{25}\)
Vì 27 > 16 nên 2725>1625
Vậy B > C
Câu 2: \(\left\{\left[\left(50-x\right):2+80\right]-5^2.2\right\}.4=200\)
\(\Leftrightarrow\left[\left(50-x\right):2+80-50\right].4=200\)
\(\Leftrightarrow\left(50-x\right):2+30=50\)
\(\Leftrightarrow\left(50-x\right):2=20\)
\(\Leftrightarrow50-x=40\)
\(\Leftrightarrow x=10\)
Vậy x = 10
\(3^{75}=\left(3^3\right)^{25}=27^{25}\)
\(2^{100}=\left(2^4\right)^{25}=8^{25}\)
Vì \(27^{25}>8^{25}\)
\(\Rightarrow3^{75}>2^{100}\)