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a, 3 x - 2 3 = 2 . 32
3 x - 2 3 = 64
3 x - 2 3 = 4 3
3 x - 2 = 4 ⇔ x = 2
b, 5 x + 1 - 5 x = 500
5 x . 5 - 5 x = 500
5 x . ( 5 - 1 ) = 500
5 x . 4 = 500
5 x = 125 = 5 3
x = 3
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] \(x^2=x^4\)
\(\Rightarrow x=x^2\)
\(\Rightarrow x-x^2=0\)
\(\Rightarrow x\left(1-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
\(a,12\left(x-1\right)=0\\ x-1=0\\ x=1\\ b,45+5\left(x-3\right)=70\\ 5\left(x-3\right)=25\\ x-3=5\\ x=8\\ c,3.x-18:2=12\\ 3.x-9=12\\ 3.x=21\\ x=7\)
\(A.3x-\frac{3}{2}-5x+\frac{10}{3}=1\)
\(3x-\frac{3}{2}-5x=-\frac{7}{3}\)
\(3x-5x=-\frac{7}{3}+\frac{3}{2}\)
\(-2x=-\frac{5}{6}\)
\(x=-\frac{5}{6}:\left(-2\right)\)
\(x=\frac{5}{12}\)
a) (3.x - 2)3 = 2.32
=> (3.x - 2)3 = 64 = 43
=> 3.x - 2 = 4
=> 3.x = 6
=> x = 2.
b) 5x+1 - 5x = 500
=>5x.5 - 5x = 500
=> 5x.(5 - 1) = 500
=> 5x.4 = 500
=> 5x = 125 = 53
=> x = 3
\(a,\left(3.x-2\right)^3=2.32\)
\(\Rightarrow\left(3x-2\right)^3=64\)
\(\Rightarrow\left(3x-2\right)^3=4^3\)
\(\Rightarrow3x-2=4\)
\(\Rightarrow3x=4+2=6\)
\(\Rightarrow x=2\)
\(b,5^{x+1}-5^x=500\)
\(\Rightarrow5^x.5-5^x=500\)
\(\Rightarrow5^x\left(5-1\right)=500\)
\(\Rightarrow5^x=500:4=125=5^3\)
\(\Rightarrow x=3\)