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NN
2
11 tháng 4 2017
a, 22x+1 = 83.165
=> 22x+1 = (23)3 . (24)5
=> 22x+1 = 29 . 220
=> 22x+1 = 229
=> 2x+1 = 29 ( vì cơ số 2 > 0 )
=> 2x = 29 - 1
=> 2x = 28
=> x = 28 : 2
=> x = 14
Vậy x = 14
11 tháng 4 2017
Ta có : \(6.2^{12}+2^{13}=3.2.2^{12}+2^{13}=3.2^{13}+2^{13}=2^{13}\left(3+1\right)=2^{13}.4=2^{13}.2^2=2^{15}=\left(2^3\right)^5=8^5\)\(3^{10}=\left(3^2\right)^5=9^5\)
Vì 8 < 9
=> 85 < 95 ( vì 5 > 0 )
=> 6.212 + 213 < 310
Vậy 6.212 + 213 < 310
15 tháng 8 2017
\(\dfrac{1-x}{2017}+\dfrac{2-x}{2016}=\dfrac{3-x}{2015}+\dfrac{4-x}{2014}\)
\(\Leftrightarrow\left(\dfrac{1-x}{2017}+1\right)+\left(\dfrac{2-x}{2016}+1\right)=\left(\dfrac{3-x}{2015}+1\right)+\left(\dfrac{4-x}{2014}+1\right)\)
\(\Leftrightarrow\dfrac{2018-x}{2017}+\dfrac{2018-x}{2016}=\dfrac{2018-x}{2015}+\dfrac{2018-x}{2014}\)
\(\Leftrightarrow\dfrac{2018-x}{2017}+\dfrac{2018-x}{2016}-\dfrac{2018-x}{2015}-\dfrac{2018-x}{2014}=0\)
\(\Leftrightarrow\left(2018-x\right)\left(\dfrac{1}{2017}+\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}\right)=0\)
Mà \(\dfrac{1}{2017}+\dfrac{1}{2016}-\dfrac{1}{2015}-\dfrac{1}{2014}\ne0\)
\(\Leftrightarrow2018-x=0\Leftrightarrow x=2018\)
Vậy ....
MV
24 tháng 7 2017
\(x:\dfrac{1}{2}+x:\dfrac{1}{4}+x:\dfrac{1}{8}+...+x:\dfrac{1}{512}=511\\ 2x+4x+8x+..+512x=511\\ x\left(2+4+8+...+512\right)=511\\ x\left(2^1+2^2+2^3+...+2^9\right)=511\\ \)
Gọi \(S=2^1+2^2+2^3+...+2^9\)
\(2S=2^2+2^3+2^4+...+2^{10}\\ 2S-S=\left(2^2+2^3+2^4+...+2^{10}\right)-\left(2^1+2^2+2^3+...+2^9\right)\\ S=2^{10}-2\)
\(x\left(2^{10}-2\right)=511\\ 2x\left(2^9-1\right)=511\\ 2x\left(512-1\right)=511\\ 2x\cdot511=511\\ 2x=1\\ x=\dfrac{1}{2}\)
Vậy \(x=\dfrac{1}{2}\)
21 tháng 5 2022
1: \(=-\dfrac{7}{80}\cdot\dfrac{4}{7}-\dfrac{2}{9}:\dfrac{16}{3}+\dfrac{5}{24}\cdot\left(\dfrac{-50+38}{15}\right)^2\)
\(=\dfrac{-1}{20}-\dfrac{2}{9}\cdot\dfrac{3}{16}+\dfrac{5}{24}\cdot\dfrac{16}{25}\)
\(=\dfrac{-1}{20}-\dfrac{1}{24}+\dfrac{2}{15}\)
\(=\dfrac{-6-5+16}{120}=\dfrac{5}{120}=\dfrac{1}{24}\)
2: \(=1500-\left\{10^3-11\cdot\left[49-5\cdot8\right]\right\}\)
\(=1500-\left\{1000-11\cdot9\right\}\)
\(=1500-1000+99=599\)
DH
24 tháng 7 2017
\(-\dfrac{2}{5}+\dfrac{5}{3}\left(\dfrac{3}{2}-\dfrac{4}{15}x\right)=-\dfrac{7}{6}\)
\(\Rightarrow\dfrac{5}{3}\left(\dfrac{3}{2}-\dfrac{4}{15}x\right)=-\dfrac{23}{30}\)
\(\Rightarrow\dfrac{3}{2}-\dfrac{4}{15}x=-\dfrac{23}{50}\)
\(\Rightarrow\dfrac{4}{15}x=\dfrac{49}{25}\Rightarrow x=\dfrac{147}{20}\)
Chúc bạn học tốt!!!
10 tháng 3 2018
Ta có: 1/3 + −2/5+ 1/6 + −1/5 ≤ x < −3/4+2/7+-1/4+3/5+5/7
⇒10-12+5-6/30≤ x< -105+40-35+84+100/140
⇒-3/30≤ x <84/140
⇒-0,1≤ x < 0,6
⇒x=0
19 tháng 6 2017
Số số hạng là :
(2x - 2) : 2 + 1 = x - 1 + 1 = x (số)
Tổng là :
(2x + 2).x : 2 = 210
=> (2x2 + 2x) : 2 = 210
=> x2 + x = 210
=> x(x + 1) = 210
=> x(x + 1) = 20.21
=> x = 20
Vậy x = 20
19 tháng 6 2017
Ta có : \(\frac{x}{2}=\frac{10}{x+1}\)
=> x(x + 1) = 10.2
=> x(x + 1) = 20
=> sai đề
Q
2 tháng 4 2017
a) \(\dfrac{-3}{8}-\dfrac{1}{8}:x=-5\dfrac{1}{4}-2\dfrac{1}{4}\)
\(\dfrac{-3}{8}-\dfrac{1}{8}:x=\dfrac{-21}{4}-\dfrac{9}{4}\)
\(\dfrac{-3}{8}-\dfrac{1}{8}:x=\dfrac{-15}{2}\)
\(\dfrac{1}{8}:x=\dfrac{-3}{8}-\dfrac{-15}{2}\)
\(\dfrac{1}{8}:x=\dfrac{57}{8}\)
\(x=\dfrac{1}{8}:\dfrac{57}{8}\)
\(x=\dfrac{1}{57}\)
b) \(\left(1\dfrac{1}{3}-25\%-\dfrac{5}{12}\right)-2x=1,6:\dfrac{3}{5}\)
\(\left(1\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{5}{12}\right)-2x=\dfrac{8}{5}:\dfrac{3}{5}\)
\(\left(\dfrac{4}{3}-\dfrac{1}{4}-\dfrac{5}{12}\right)-2x=\dfrac{8}{3}\)
\(\left(\dfrac{13}{12}-\dfrac{5}{12}\right)-2x=\dfrac{8}{3}\)
\(\dfrac{2}{3}-2x=\dfrac{8}{3}\)
\(2x=\dfrac{2}{3}-\dfrac{8}{3}\)
\(2x=-2\)
\(x=\left(-2\right):2\)
\(x=-1\)
7 tháng 4 2017
Câu 1:
a) \(-\dfrac{2}{3}\left(x-\dfrac{1}{4}\right)=\dfrac{1}{3}\left(2x-1\right)\)
\(\Rightarrow-\dfrac{2}{3x}+\dfrac{1}{6}=\dfrac{2}{3}x-\dfrac{1}{3}\)
\(\Rightarrow\dfrac{2}{3}x+\dfrac{2}{3}x=\dfrac{1}{6}+\dfrac{1}{3}\)
\(\Rightarrow x.\left(\dfrac{2}{3}+\dfrac{2}{3}\right)=\dfrac{1}{2}\)
\(\Rightarrow x.\dfrac{4}{3}=\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{1}{2}:\dfrac{4}{3}\)
\(\Rightarrow x=\dfrac{3}{8}\)
\(\dfrac{2^{2x-3}}{4^{10}}=8^3.16^5\)
\(\Rightarrow2^{2x-3}=8^3.16^5.4^{10}\)
\(\Rightarrow2^{2x-3}=2^9.2^{20}.2^{20}\)
\(\Rightarrow2^{2x-3}=2^{49}\)
Vì \(2\ne\pm1;2\ne0\) nên \(2x-3=49\)
\(\Rightarrow2x=52\Rightarrow x=26\)
Vậy..........
Chúc bạn học tốt!!!