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a, \(2.x^x=10.3^{12}+8.27^4\)
\(2.x^x=10.3^{12}+8.3^{12}\)
\(2.x^x=3^{12}.\left(10+8\right)\)
\(2.x^x=3^{12}.18\)
\(2.x^x=3^{12}.2.3^3\)
\(2.x^x=3^{15}.2\)
\(x^x=3^{15}\)( Hình như sai đề )
b,\(3^{2x+2}=9^{x+3}\)
\(3^{2x+2}=3^{2x+3}\)
a; => \(3^x+3^x.3+3^x.3^2=1053\)
=> \(3^x.\left(1+3+3^2\right)=1053\)
=> \(3^x.13=1053\)
=> \(3^x=81\)
=> \(3^x=3^4\)
=> x=4
b; => (x-1)^2.(x-1)=(x-1)^2
=> (x-1)^2.(x-1)-(x-1)^2=0
=> (x-1)^2.[(x-1)^2-1)=0
\(\hept{\begin{cases}x-1=0\\x-1=1\\x-1=-1\end{cases}}\)
=> \(\hept{\begin{cases}x=1\\x=2\\x=0\end{cases}}\)
Đề đúng là 3x+3x+1+3x+2=1053
\(\Rightarrow3^x\left(1+3^1+3^2\right)=1053\)
\(\Rightarrow3^x\cdot13=1053\)
\(\Rightarrow3^x=81\)
\(\Rightarrow3^x=3^4\)
\(\Rightarrow x=4\)
Đề bài phải là :
\(3^x+3^{x+1}3^{x+2}=1053\)
\(3^x+3^x.3+3^x.3^2=1053\)
\(3^x.\left(1+3+3^2\right)=1053\)
\(3^x.\left(1+3+9\right)=1053\)
\(3^x.13=1053\)
\(3^x=1053:13\)
\(3^x=81\)
\(3^x=3^4\)
\(x=4\)
Chúc bạn học tốt 
ngu vip
\(a,3x+17x=340\)
\(x\left(17+3\right)=340\)
\(x20=340\)
\(x=340:20=17\)
\(b,\left|2x+1\right|=3\\ \Rightarrow\left[{}\begin{matrix}2x+1=3\\2x+1=-3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=3-1=2\\2x=-3-1=-4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
\(c,3^x+3^{x+1}+3^{x+2}=1053\\ 3^x\left(1+3+9\right)=1053\\ 3^x.13=1053\\ 3^x=1053:13=81=3^4\\ \Rightarrow x=4\)
Bài 2 :x+1/3=x-3/4 <=>4.(x+1)=3.(x-3) 4x+4=3x-9 4x-3x=-9-4 x=-13
Bài 1:
ta có: \(\frac{17}{x+1}.\frac{x}{6}=\frac{17x}{6x+6}\)
Để 17x/6x+6 thuộc Z
=> 17x chia hết cho 6x + 6
=> 102x chia hết cho 6x + 6
102x + 102 - 102 chia hết cho 6x + 6
17.(6x+6) - 102 chia hết cho 6x+6
mà 17.(6x+6) chia hết cho 6x + 6
=> 102 chia hết cho 6x + 6
=> ...
bn tự lm típ nha!
Bài 2:
ta có: \(\frac{x+1}{3}=\frac{x-3}{4}\)
\(\Rightarrow4x+4=3x-9\)
\(\Rightarrow4x-3x=-9-4\)
\(x=-13\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{5}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{5}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2}{5}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2}{5}\)
\(\frac{1}{x+1}=\frac{1}{10}\)
\(\Rightarrow x+1=10\)
\(\text{Vậy x = 9}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{2}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2}{5}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2}{5}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{10}\)
\(\Rightarrow x+1=10\)
\(\Rightarrow x=10-1\)
\(\Rightarrow x=9\)
Vẫy = 9
a) (\(\frac{10\left(10+1\right)}{2}\))2 = (x+1)2
552 = (x+1)2
55 =x+1
x = 54
xem đi, mk làm tip cau b
3x+2+3x+1+3x < 1053
3x(32+3+1) < 1053
3x . 13 < 81 . 13
=> 3x < 81
=> 3x < 34
=> x < 4
Ta có:
3x+3x+1+3x+2 =1053
=>3x+3x.3+3x.32=1053
=>3x.(1+3+32)=1053
=>3x.13=1053
=>3x =81
=>3x=34
=>x=4
Vậy x=4