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\(a)3^x\cdot81^{2x+1}=81\\ 3^x\cdot\left(3^4\right)^{2x+1}=81\\ 3^x\cdot3^{8x+4}=3^4\\ 3^{9x+4}=3^4\\ \Leftrightarrow9x+4=4\\ \Leftrightarrow9x=0\\ \Rightarrow x=0\)
\(b)4^x-25=89\\ \Leftrightarrow4^x=64\\ \Leftrightarrow4^x=4^3\\ \Rightarrow x=3\)
a) 2 + 4 + 6 + ... + 2x = 210
=> 2(1+2+3+4+...+x) = 210
1 + 2 + 3 + .. + x = 210 : 2
1 + 2 + 3 + ... + x = 105
=> Ta có: (x+1)x:2 = 105
(x+1)x = 105.2
(x+1)x = 210
=> (x+1)x = 210 = 15.14
Vậy => x = 14
a) 2+4+6+...+2x=210
<=> {[(2x-2):2+1]:2}.(2x+2) =210
<=> {[2(x-1):2+1]:2}.2(x+1) =210
<=> [(x-1)+1]:2.2(x+1) =210
<=> (x-1+1)(x+1) =210
<=> x(x+1) =210
Vì 14.15=210 nên x=14
b) x + (x - 1) + (x - 2) + ....+ (x - 50) = 255
=> x+x-1+x-2+....+x-50 = 255
=> 51.x-(1+2+3+....+50) = 255
=> 51.x - 1275 = 255
=> 51.x = 1530
=> x = 1530 : 51
=> x = 30
c) (x+1)+(x+2)+....+(x+100)=5750
=> (x+x+...+x)+(1+2+3+...+100)=5750
=> 100x + 5050 = 5750
=> 100x = 700
=> x = 700 : 100
=> x = 7
a) \(500< 2^{x+1}< 1000\Leftrightarrow2^8< 500< 2^{x+1}< 1000< 2^{10}\)
\(\Rightarrow8< x+1< 10\Rightarrow7< x< 9\)
Do x là số tự nhiên nên x = 8.
b) \(\frac{1}{16}.2^x.4^{x+2}=64\)
\(\Leftrightarrow2^x.2^{2x+4}=1024\Leftrightarrow2^{3x+4}=2^{10}\)
\(\Leftrightarrow3x+4=10\Leftrightarrow x=2\)
c.\(\dfrac{3}{7}+\dfrac{5}{7}:x=\dfrac{1}{3}\)
\(\dfrac{5}{7}:x=\dfrac{1}{3}-\dfrac{3}{7}\)
\(\dfrac{5}{7}:x=-\dfrac{2}{21}\)
\(x=\dfrac{5}{7}:-\dfrac{2}{21}\)
\(x=-\dfrac{15}{2}\)
d.\(3\dfrac{1}{4}:\left|2x-\dfrac{5}{12}\right|=\dfrac{39}{16}\)
\(\left|2x-\dfrac{5}{12}\right|=3\dfrac{1}{4}:\dfrac{39}{16}\)
\(\left|2x-\dfrac{5}{12}\right|=\dfrac{4}{3}\)
\(\rightarrow\left[{}\begin{matrix}2x-\dfrac{5}{12}=\dfrac{4}{3}\\2x-\dfrac{4}{12}=-\dfrac{4}{3}\end{matrix}\right.\) \(\rightarrow\left[{}\begin{matrix}2x=\dfrac{7}{4}\\2x=-\dfrac{11}{12}\end{matrix}\right.\) \(\rightarrow\left[{}\begin{matrix}x=\dfrac{7}{8}\\x=-\dfrac{11}{24}\end{matrix}\right.\)
A, \(\dfrac{4}{9}+x=\dfrac{5}{3}\)
\(x\)\(=\dfrac{5}{3}-\dfrac{4}{9}\)
\(x\)\(=\dfrac{11}{9}\)
B,\(\dfrac{3}{4}.x=\dfrac{-1}{2}\)
\(x=\dfrac{-1}{2}:\dfrac{3}{4}\)
\(x=\)\(\dfrac{-2}{3}\)
Chị gái xinh đẹp à. Câu hỏi của chị khó quá ko ai trả lời. Thôi thì.......k cho mem đi😉
\(b,2.3^x+3^x=27\)
\(\Leftrightarrow3^x.\left(2+1\right)=27\)
\(\Leftrightarrow3^x.3=27\)
\(\Leftrightarrow3^x=27:3\)
\(\Leftrightarrow3^x=9\)
\(\Leftrightarrow3^x=3^2\)
\(\Rightarrow x=2\)
\(3^x.81^{2x+1}=81\)
\(3^x.3^{4x+4}=3^4\)
\(3^{5x+4}=3^4\)
\(3^{5x}.3^4=3^4\)
\(\Rightarrow3^{5x}=1\)
\(3^{5x}=3^0\)
\(\Rightarrow5x=0\)
\(\Rightarrow x=0\)
Vậy \(x=0\)
\(4^x-25=89\)
\(4^x=89+25\)
\(4^x=114\)
\(4^x=2.57\)
Ta có: 2.57 không chia hết cho 4
Mà \(x\in N\)
\(\Rightarrow4^x\ne114\)
\(\Rightarrow\)x không có giá trị
Vậy x không có giá trị
b) Tham khảo bài bạn TAKASA
Tham khảo nhé~
\(a,4^x+4^{x+1}=80\)
\(\Leftrightarrow4^x.1+4^x.4^1=80\)
\(\Leftrightarrow4^x.1+4^x.4=80\)
\(\Leftrightarrow4^x.\left(1+4\right)=80\)
\(\Leftrightarrow4^x.5=80\)
\(\Leftrightarrow4^x=80:5\)
\(\Leftrightarrow4^x=16\)
\(\Leftrightarrow4^x=4^2\)
\(\Rightarrow x=2\)