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Bài 1:
\(\text{a) }x.x^2.x^3.x^4.x^5.....x^{49}.x^{50}\)
\(=x^{1+2+3+4+5+...+49+50}\)
\(=x^{\frac{51.50}{2}}\)
\(=x^{1275}\)
\(\text{b) Ta có:}\)
\(4^{15}=\left(2^2\right)^{15}=2^{2.15}=2^{30}\)
\(8^{11}=\left(2^3\right)^{11}=2^{3.11}=2^{33}\)
\(\text{Vì }2^{30}< 2^{33}\text{ nên }4^{15}< 8^{11}\)
Bài 2: Tìm x
\(\left(x-1\right)^4:3^2=3^6\)
\(\Rightarrow\left(x-1\right)^4=3^6\times3^2\)
\(\Rightarrow\left(x-1\right)^4=3^8\)
\(\Rightarrow\left(x-1\right)^4=3^{2.4}\)
\(\Rightarrow\left(x-1\right)^4=\left(3^2\right)^4\)
\(\Rightarrow x-1=9\)
\(\Rightarrow x=10\)
Bài 3 và bài 4 mk làm sau
Bài 1 : a) \(x.x^2.x^3.x^4.....x^{49}.x^{50}=x^{1+2+3+...+49+50}\) (Dễ rồi tự tính)
b) \(\hept{\begin{cases}4^{15}=\left(2^2\right)^{15}=2^{30}\\8^{11}=\left(2^3\right)^{11}=2^{33}\end{cases}}\)Rồi tự so sánh đi
Bài 2 :
\(\left(x-1\right)^4\div3^2=3^6\Leftrightarrow\left(x-1\right)^4=3^8=\left(3^2\right)^4=9^4\Leftrightarrow x-1=9\Leftrightarrow x=10\)
Bài 3 :
\(\hept{\begin{cases}27^{15}=\left(3^3\right)^{15}=3^{45}\\81^{11}=\left(3^4\right)^{11}=3^{44}\end{cases}}\) nt
a, \(2\cdot2^2\cdot2^3\cdot2^4\cdot...\cdot2^x=1024\)
\(\Leftrightarrow2^{1+2+3+4+...+x}=2^{10}\Leftrightarrow1+2+3+4+...+x=10\)
\(\Rightarrow\left(x+1\right)x\div2=10\Rightarrow\left(x+1\right)x=20\)
Vì : ( x + 1 ) x là hai số tự nhiên liên tiếp \(\Rightarrow x=4\in Z\)
Vậy x = 4
b, \(9.27< 3^x< 243\Leftrightarrow3^5< 3^x< 3^5\)
\(\Rightarrow5< x< 5\Rightarrow x\in\varnothing\)
Vậy \(x\in\varnothing\)
1.Tim x:
a)| x + 1 | = 5 -> Th1: x+1=5-> x= 5-1=4
Th2: x+1=-5-> x= (-5) -1=-6(Loại. vì x lớn hơn hoặc bằng 0)
Vậy x= 4
b)| x - 3 | = 7 -> TH1: x-3=7-> x=7+3=10(Loại. Vì x<3)
TH2: x-3=-7-> x=-7+3=-4
Vậy x= -4
c) x + | 2 - x | = 6
-> | 2 - x | =6 -x
-> TH1: 2-x = 6-x
-> -x+ x= 2-6
-> 0x =-4(LOẠI)
TH2: 2-x= -6+x
->(-x)-x= 2+6
-> -2.x=8
-> x=8: -2=-4
Vậy x=-4
Tick cho mik nha!!!
2. Tìm x
a) | x | = 7-> x=-7 hoặc x=7
b) | x | < 7.Vì| x | lớn hơn hoặc bằng 0
-> | x | =(0;1;2;3;4;5;6)
-> x= (-6;-5;-4;-3;-2;-1;0;1;2;3;4;5;6)
c) | x | > 7
-> | x | =(8;9;10;11;12;13.............)
-> x= (...............;-9;-8;8;9;10;.............)
1. Ta có \(\frac{n^2-2n+3}{n-2}=\frac{n\left(n-2\right)+3}{n-2}=n+\frac{3}{n-2}\)
Để \(\frac{n^2-2n+3}{n-2}\in Z\) thì \(\frac{3}{n-2}\in Z\Rightarrow n-2\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\)
\(\Rightarrow n\in\left\{-1;1;3;5\right\}\)
2. \(\frac{x}{4}=\frac{10}{x+3}\)
ĐK: \(x\ne-3\)
\(\frac{x}{4}=\frac{10}{x+3}\)
\(\Leftrightarrow\frac{x}{4}-\frac{10}{x+3}=0\)
\(\Leftrightarrow\frac{x^2+3x-40}{4\left(x+3\right)}=0\)
\(\Leftrightarrow x^2+3x-40=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=5\\x=-8\end{cases}}\left(tmđk\right)\)
b) \(\frac{x+2}{7}=\frac{-49}{\left(x+2\right)^2}\)
ĐK: \(x\ne-2\)
\(\frac{x+2}{7}=\frac{-49}{\left(x+2\right)^2}\)
\(\Leftrightarrow\left(x+2\right)^3=-49.7\)
\(\Leftrightarrow\left(x+2\right)^3=-343\)
\(\Leftrightarrow x+2=-7\)
\(\Leftrightarrow x=-9\left(tmđk\right)\)
bn Huyền ơi ở câu 1 bn chép sai đầu bài của bạn Thảo rùi
a, \(5^x=625\Rightarrow5^x=5^4\Rightarrow x=4\)
b, \(4^{2x-6}=1\Rightarrow4^{2x-6}=4^0\)
\(\Rightarrow2x-6=0\Rightarrow x=3\)
c, \(\left(3x-1\right)^3=8\Rightarrow3x-1=2\)
\(\Rightarrow x=1\)
d, \(49.7^n=2401\Rightarrow7^{n+2}=7^4\)
\(\Rightarrow n+2=4\Rightarrow n=2\)
e, \(x^4.x-27.x=0\)
\(\Rightarrow x\left(x^4-27\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^4-27=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=\pm\sqrt[4]{27}\end{cases}}\)
f, \(\left(x-6\right)^3=\left(x-6\right)^2\)
\(\Rightarrow\left(x-6\right)^3-\left(x-6\right)^2=0\)
\(\Rightarrow\left(x-6\right)^2\left(x-6-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-6=0\\x-7=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=6\\x=7\end{cases}}\)
Chúc bạn học tốt!!!
\(a,5^x=625\) \(b,4^{2x-6}=1\)
\(\Rightarrow5^x=5^4\) \(\Rightarrow2x-6=0\) (Vì mọi số mũ không bằng 1)
\(\Rightarrow x=4\) \(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
\(c,\left(3x-1\right)^3=8\) \(d,49.7^n=2401\)
\(\Rightarrow\left(3x-1\right)^3=2^3\) \(\Rightarrow7^n=2401:49\)
\(\Rightarrow3x-1=2\) \(\Rightarrow7^n=49\)
\(\Rightarrow3x=3\) \(\Rightarrow7^n=7^2\)
\(\Rightarrow x=1\) \(\Rightarrow n=2\)
\(e,x^4.x-27.x=0\)
\(\Rightarrow x.\left(x^4-27\right)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\x^4-27=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x^4=27\end{cases}}}\)
\(f,\left(x-6\right)^3=\left(x-6\right)^2\)
\(\Rightarrow x.\left(x^4-27\right)=0\) \(\Rightarrow\hept{\begin{cases}\left(x-6\right)^3=\left(x-6\right)^2\\\left(x-6\right)^3=\left(x-6\right)^2\end{cases}\Rightarrow\hept{\begin{cases}\left(x-6\right)^3:\left(x-6\right)^2=1\\\left(x-6\right)^3-\left(x-6\right)^2=0\end{cases}\Rightarrow}\hept{\begin{cases}x-6=1\\x-6=0\end{cases}}\Rightarrow\hept{\begin{cases}x=7\\x=6\end{cases}}}\)
