1) B = \(\frac{4^2.2^3}{2^6}\)
2) Tìm x;y biết : \(\frac{x}{5}=\frac{y}{7}\)và 2y - x = 27
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14 tháng 7 2016
b./ \(\Leftrightarrow\frac{x+1}{2009}+1+\frac{x+2}{2008}+1+\frac{x+3}{2007}+1=\frac{x+10}{2000}+1+\frac{x+11}{1999}+1+\frac{x+12}{1998}+1.\)
\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}-\frac{x+2010}{2000}-\frac{x+2010}{1999}-\frac{x+2010}{1998}=0\)
\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}\right)=0\)(b)
Mà \(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2000}-\frac{1}{1999}-\frac{1}{1998}< 0\)
(b) \(\Leftrightarrow x+2010=0\Leftrightarrow x=-2010\)
14 tháng 7 2016
a./
\(\Leftrightarrow\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}-\frac{x+1}{5}-\frac{x+1}{6}=0.\)
\(\Leftrightarrow\left(x+1\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)=0\)(a)
Mà \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}>0\)
(a) \(\Leftrightarrow x+1=0\Leftrightarrow x=-1\)
16 tháng 2 2021
a) \(x+\left(-7\right)=-20\)
\(\Rightarrow x=-20+7\)
\(\Rightarrow x=-13\)
Vậy \(x=-13\)
b) \(8-x=-12\)
\(\Rightarrow x=8-\left(-12\right)\)
\(\Rightarrow x=20\)
Vậy \(x=20\)
c) \(|x|-7=-6\)
\(\Rightarrow|x|=-6+7\)
\(\Rightarrow|x|=1\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
Vậy \(x\in\left\{1;-1\right\}\)
d) \(5^2.2^2-7.|x|=65\)
\(\Rightarrow\left(5.2\right)^2-7.|x|=65\)
\(\Rightarrow10^2-7.|x|=65\)
\(\Rightarrow100-7.|x|=65\)
\(\Rightarrow7.|x|=35\)
\(\Rightarrow|x|=5\)
\(\Rightarrow\orbr{\begin{cases}x=5\\x=-5\end{cases}}\)
Vậy \(x\in\left\{5;-5\right\}\)
e) \(37-3.|x|=2^3-4\)
\(\Rightarrow37-3.|x|=8-4\)
\(\Rightarrow37-3.|x|=4\)
\(\Rightarrow3.|x|=33\)
\(\Rightarrow|x|=11\)
\(\Rightarrow\orbr{\begin{cases}x=11\\x=-11\end{cases}}\)
Vậy \(x\in\left\{11;-11\right\}\)
f) \(|x|+|-5|=|-37|\)
\(\Rightarrow|x|+5=37\)
\(\Rightarrow|x|=32\)
\(\Rightarrow\orbr{\begin{cases}x=32\\x=-32\end{cases}}\)
Vậy \(x\in\left\{32;-32\right\}\)
g)\(5.|x+9|=40\)
\(\Rightarrow|x+9|=8\)
\(\Rightarrow\orbr{\begin{cases}x+9=8\\x+9=-8\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-1\\x=-17\end{cases}}\)
Vậy \(x\in\left\{-1;-17\right\}\)
h) \(-\frac{5}{6}+\frac{8}{3}+\frac{-29}{6}\le x\le\frac{-1}{2}+2+\frac{5}{2}\)
\(\Rightarrow\frac{-5}{6}+\frac{16}{6}+\frac{-29}{6}\le x\le\frac{-1}{2}+\frac{4}{2}+\frac{5}{2}\)
\(\Rightarrow-3\le x\le4\)
Vậy \(-3\le x\le4\)
20 tháng 8 2017
Bài 1 )
a ) \(2.2^2.2^3.....2^x=1024\Leftrightarrow2^{1+2+....+x}=2^{10}\Leftrightarrow1+2+....+x=10\)
\(\Leftrightarrow\frac{x\left(x+1\right)}{2}=10\Leftrightarrow\left(x+1\right)x=20=4.5\Rightarrow x=4\)
b ) \(\frac{37-x}{x+13}=\frac{3}{7}\Leftrightarrow3x+39=259-7x\Leftrightarrow3x+7x=259-39\Leftrightarrow10x=220\Rightarrow x=22\)
Bài 2 ) \(\frac{1}{2}\sqrt{64}-\sqrt{\frac{4}{25}}+\left(\frac{50^2-15.125}{5^4}\right)^{2014}=\frac{1}{2}.8-\frac{2}{5}+\left(\frac{5^4.2^2-3.5^4}{5^4}\right)^{2014}\)
\(=4-\frac{2}{5}+\left[\frac{5^4\left(4-3\right)}{5^4}\right]^{2014}=\frac{18}{5}+1=\frac{23}{5}\)
20 tháng 8 2017
Mình làm bài 1 thui nha, còn bài 2 thì còn tự tính là được thôi mừ !!!
Bài 1:
a) \(2.2^2.2^3...2^x=1024\)
\(=>2^{1+2+3+...+x}=2^{10}\)
\(< =>1+2+3+...+x=10\)
\(=>6+x=10\)
\(=>x=10-6\)
\(=>x=4.\)
Nếu đúng thì k cho mình nhá
TV
4
HP
2 tháng 10 2021
3-2 . 34 . 3x = 37
<=> 32 + x = 37
<=> 2 + x = 7
<=> x = 7 - 2
<=> x = 5
2 tháng 10 2021
\(2^{-2}\cdot2^x+2\cdot2^x=9\cdot2^6\\ \Rightarrow2^{x-2}+2^{x+1}=9\cdot2^6\\ \Rightarrow2^{x-2}\left(1+2^3\right)=9\cdot2^6\\ \Rightarrow2^{x-2}\cdot9=9\cdot2^6\Rightarrow2^{x-2}=2^6\\ \Rightarrow x-2=6\Rightarrow x=8\)
\(3^{-2}\cdot3^4\cdot3^x=3^7\\ \Rightarrow3^{x+4-2}=3^7\\ \Rightarrow x+2=7\Rightarrow x=5\)
28 tháng 8 2021
a) \(\frac{\left(5.2\right)}{3.2}-\frac{1}{2}x+\frac{1}{3}+\frac{1}{5}=\frac{\left(3.2\right)}{5}\)
\(\Leftrightarrow\)\(\frac{1}{2}-\frac{1}{2}x+\frac{8}{15}=\frac{6}{5}\)
\(\Leftrightarrow\)\(\frac{1}{2}-\frac{2}{3}=\frac{1}{2}x\)
\(\Leftrightarrow\)\(-\frac{1}{6}=\frac{1}{2}x\)
\(\Leftrightarrow\)x=-1/3
28 tháng 8 2021
b) VT= \(\frac{\left(3.5.4.2\right)}{5.2.3}=4\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right):6+4=4:\frac{2}{3}=6\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right):6=2\)
\(\Leftrightarrow x-\frac{1}{2}=12\)
=> x= 12,5
12 tháng 7 2019
a)\(\left(\frac{1}{3}\right)^{-1}-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^4.2^3=3-1+\frac{1}{16}.8=3-1+\frac{1}{2}=\frac{5}{2}\\ \)
b)\(2^2.2^3.\left(\frac{2}{3}\right)^{-2}=2^5.\frac{9}{4}=72\)
c)\(\left(\frac{4}{3}\right)^{-2}.\left(\frac{3}{4}\right)^3:\left(\frac{-2}{3}\right)^{-3}=\left(\frac{3}{4}\right)^2.\left(\frac{3}{4}\right)^3:\left(\frac{-2}{3}\right)^{-3}=\left(\frac{3}{4}\right)^5:\left(\frac{3}{2}\right)^3=\frac{9}{128}\)
2)
\(3^{x+1}=9^x\Leftrightarrow3^x.3=9^x\Rightarrow3=9^x:3^x\Rightarrow3=3^x\Rightarrow x=1\)
\(\left(x-0,1\right)^2=6,25\Leftrightarrow\left(x-0,1\right)^2=2,5^2\Rightarrow\left(x-0,1\right)=2,5\Rightarrow x=2,5+0,1=2,6\)
\(3^{2x-1}=243\Leftrightarrow3^{2x-1}=3^5\Rightarrow2x-1=5\Rightarrow2x=6\Rightarrow x=3\)
\(\left(4x-3\right)^4=\left(4x-3\right)^2\Rightarrow x=1\)
\(b,B=\frac{4^2\cdot2^3}{2^6}\)
\(=\frac{2^4\cdot2^3}{2^6}\)
\(=\frac{2^7}{2^6}=2\)
\(b,\frac{x}{5}=\frac{y}{7}\Rightarrow\frac{x}{5}=\frac{2y}{14}\)
ap dụng tính chất DTSBN ta có
\(\frac{2y}{14}=\frac{x}{5}=\frac{2y-x}{14-5}=\frac{27}{9}=3\)
\(\hept{\begin{cases}\frac{x}{5}=3\Rightarrow x=15\\\frac{y}{7}=3\Rightarrow y=21\end{cases}}\)
1)
\(B=\frac{4^2.2^3}{2^6}=\frac{\left(2^2\right)^2.2^3}{2^6}=\frac{2^4.2^3}{2^6}=\frac{2^7}{2^6}=2\)
2)
Áp dụng tính chất dãy tỉ số bằng nhau ta được :
\(\frac{x}{5}=\frac{y}{7}=\frac{2y}{14}=\frac{2y-x}{14-5}=\frac{27}{9}=3\)
\(\Rightarrow\hept{\begin{cases}x=3.5=15\\y=3.7=21\end{cases}}\)