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24 tháng 12 2016
Bài 2:
a) \(x+\frac{1}{3}=\frac{3}{4}\)
\(\Rightarrow x=\frac{5}{12}\)
Vậy \(x=\frac{5}{12}\)
b) \(\left|x+\frac{1}{8}\right|-\frac{1}{6}=0\)
\(\Rightarrow\left|x+\frac{1}{8}\right|=\frac{1}{6}\)
\(\Rightarrow x+\frac{1}{8}=\frac{1}{6}\) hoặc \(x+\frac{1}{8}=\frac{-1}{6}\)
+) \(x+\frac{1}{8}=\frac{1}{6}\Rightarrow x=\frac{1}{24}\)
+) \(x+\frac{1}{8}=\frac{-1}{6}\Rightarrow x=\frac{-7}{24}\)
Vậy \(x\in\left\{\frac{1}{24};\frac{-7}{24}\right\}\)
c) \(\frac{x}{27}=\frac{-2}{36}\)
\(\Rightarrow\frac{x}{27}=\frac{-1}{18}\)
\(\Rightarrow18x=-27\)
\(\Rightarrow x=\frac{-3}{2}\)
Vậy \(x=\frac{-3}{2}\)
d) \(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)
\(\Rightarrow x+\frac{1}{2}=\frac{1}{4}\) hoặc \(x+\frac{1}{2}=\frac{-1}{4}\)
+) \(x+\frac{1}{2}=\frac{1}{4}\Rightarrow x=\frac{-1}{4}\)
+) \(x+\frac{1}{2}=\frac{-1}{4}\Rightarrow x=\frac{-3}{4}\)
Vậy \(x\in\left\{\frac{-1}{4};\frac{-3}{4}\right\}\)
24 tháng 12 2016
a)\(x+\frac{1}{3}=\frac{3}{4}\)
\(\Rightarrow x=\frac{3}{4}-\frac{1}{3}\)
\(\Rightarrow x=\frac{5}{12}\)
b)\(\left|x+\frac{1}{8}\right|-\frac{1}{6}=0\)
\(\Rightarrow\left|x+\frac{1}{8}\right|=\frac{1}{6}\)
\(\Rightarrow x+\frac{1}{8}=\frac{1}{6}\) hoặc \(x+\frac{1}{8}=-\frac{1}{6}\)
\(\Rightarrow x=\frac{1}{6}-\frac{1}{8}\) hoặc \(x=-\frac{1}{6}-\frac{1}{8}\)
\(\Rightarrow x=\frac{1}{24}\) hoặc \(x=-\frac{7}{24}\)
c)\(\frac{x}{27}=-\frac{2}{36}\)
\(\Rightarrow x=\frac{\left(-2\right)\cdot27}{36}=-\frac{3}{2}\)
d)\(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)
\(\Rightarrow\left(x+\frac{1}{2}\right)^2=\left(\frac{1}{4}\right)^2=\left(-\frac{1}{4}\right)^2\)
\(\Rightarrow x+\frac{1}{2}=\frac{1}{4}\) hoặc \(x+\frac{1}{2}=-\frac{1}{4}\)
\(\Rightarrow x=\frac{1}{4}-\frac{1}{2}\) hoặc \(x=-\frac{1}{4}-\frac{1}{2}\)
\(\Rightarrow x=-\frac{1}{4}\) hoặc \(x=-\frac{3}{4}\)
29 tháng 11 2016
a)\(\left(-3\right)^{x+3}=-\frac{1}{27}\)
\(\left(-3\right)^{x+3}=\left(-\frac{1}{3}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-\frac{3^0}{3^1}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-3^{-1}\right)^3\)
\(\left(-3\right)^{x+3}=\left(-3\right)^{-3}\)
\(\Rightarrow x+3=-3\)
\(\Rightarrow x=-6\)
b)\(\left(-6\right)^{2x+2}=\frac{1}{36}\)
\(\left(-6\right)^{2x+2}=\left(-\frac{1}{6}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-\frac{6^0}{6^1}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-6^{-1}\right)^2\)
\(\left(-6\right)^{2x+2}=\left(-6\right)^{-2}\)
\(\Rightarrow2x+2=-2\)
\(\Rightarrow2x=-4\)
\(\Rightarrow x=-2\)
c)\(\left(-3\right)^{x+5}=\frac{1}{81}\)
\(\left(-3\right)^{x+5}=\left(-\frac{1}{3}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-\frac{3^0}{3^1}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-3^{-1}\right)^4\)
\(\left(-3\right)^{x+5}=\left(-3\right)^{-4}\)
\(\Rightarrow x+5=-4\)
\(\Rightarrow x=-9\)
29 tháng 11 2016
d)\(\left(\frac{1}{9}\right)^x=\left(\frac{1}{27}\right)^6\)
\(\left[\left(\frac{1}{3}\right)^2\right]^x=\left[\left(\frac{1}{3}\right)^3\right]^6\)
\(\left(\frac{1}{3}\right)^{2x}=\left(\frac{1}{3}\right)^{18}\)
\(\Rightarrow2x=18\)
\(\Rightarrow x=9\)
e)\(\left(\frac{4}{9}\right)^x=\left(\frac{8}{27}\right)^6\)
\(\left[\left(\frac{2}{3}\right)^2\right]^x=\left[\left(\frac{2}{3}\right)^3\right]^6\)
\(\left(\frac{2}{3}\right)^{2x}=\left(\frac{2}{3}\right)^{18}\)
\(\Rightarrow2x=18\)
\(\Rightarrow x=9\)
VM
24 tháng 8 2019
a) Ta có: \(\frac{x}{12}=\frac{y}{3}.\)
=> \(\frac{x}{12}=\frac{y}{3}\) và \(x-y=36.\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{x}{12}=\frac{y}{3}=\frac{x-y}{12-3}=\frac{36}{9}=4.\)
\(\left\{{}\begin{matrix}\frac{x}{12}=4=>x=4.12=48\\\frac{y}{3}=4=>y=4.3=12\end{matrix}\right.\)
Vậy \(\left(x;y\right)=\left(48;12\right).\)
b)
\(\frac{2}{3}+\frac{5}{3}x=\frac{5}{7}\)
⇒ \(\frac{5}{3}x=\frac{5}{7}-\frac{2}{3}\)
⇒ \(\frac{5}{3}x=\frac{1}{21}\)
⇒ \(x=\frac{1}{21}:\frac{5}{3}\)
⇒ \(x=\frac{1}{35}\)
Vậy \(x=\frac{1}{35}.\)
\(\left(x-\frac{1}{2}\right)^3=\frac{1}{27}\)
⇒ \(\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{3}\right)^3\)
⇒ \(x-\frac{1}{2}=\frac{1}{3}\)
⇒ \(x=\frac{1}{3}+\frac{1}{2}\)
⇒ \(x=\frac{5}{6}\)
Vậy \(x=\frac{5}{6}.\)
Có 1 câu bạn đăng mình làm ở dưới rồi mà.
Chúc bạn học tốt!
24 tháng 8 2019
a)áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{x}{12}=\frac{y}{3}=\frac{x-y}{12-3}=\frac{36}{9}=4\)
\(\)x/12=4 suy ra x=12.4=48
y/3=4 suy ra y=3.4 =12
b)\(\frac{2}{3}+\frac{5}{3}x=\frac{5}{7}\)
\(\frac{5}{3}x=\frac{5}{7}-\frac{2}{3}\)
\(\frac{5}{3}x=\frac{1}{21}\)
\(x=\frac{1}{21}:\frac{5}{3}\)
\(x=\frac{1}{35}\)
\(\frac{11}{12}-\left(\frac{2}{5}+x\right)=\frac{2}{3}\)
\(\left(\frac{2}{5}+x\right)=\frac{11}{12}-\frac{2}{3}\)
\(\frac{2}{5}+x=\frac{1}{4}\)
\(x=\frac{1}{4}-\frac{2}{5}\)
\(x=\frac{-3}{20}\)
\(\left|x-\frac{2}{5}\right|+\frac{3}{4}=\frac{11}{4}\)
\(\left|x-\frac{2}{5}\right|=\frac{11}{4}-\frac{3}{4}\)
\(\left|x-\frac{2}{5}\right|=2\)
suy ra x-2/5=2 hoac x-2/5=-2
\(x-\frac{2}{5}=2\)
\(x=\frac{12}{5}\)
\(x-\frac{2}{5}=-2\)
\(x=\frac{-8}{5}\)
\(\left(x-\frac{1}{2}\right)^3=\frac{1}{27}\)
\(\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{3}\right)^3\)
\(x-\frac{1}{2}=\frac{1}{3}\)
\(x=\frac{1}{3}+\frac{1}{2}\)
\(x=\frac{5}{6}\)
XO
27 tháng 9 2020
Ta có :\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
=> \(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)
=> \(2\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)
=> \(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)
=> \(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)
=> \(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)
=> \(\frac{1}{x+1}=\frac{1}{18}\)
=> x + 1 = 18
=> x = 17
Vậy x = 17
TT
9 tháng 10 2020
a) Theo t/c dãy tỉ số bằng nhau:
\(\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{27}{7}\)
+) \(\frac{x}{2}=\frac{27}{7}\)=> x= (27x2) : 7 =\(\frac{54}{7}\)
+) \(\frac{y}{5}=\frac{27}{7}\)=> y= (27x5) : 7 = \(\frac{135}{7}\)
Vậy x=\(\frac{54}{7}\); y=\(\frac{135}{7}\)
b) Tương tự câu a
\(\frac{x}{3}=\frac{y}{6}=\frac{x+y}{3+6}=\frac{27}{9}=3\)
+) \(\frac{x}{3}=3\)=> x= 3x3 = 9
+) \(\frac{y}{6}=3\)=> y= 3x6 = 18
Vậy x= 9 ; y= 18
PN
9 tháng 10 2020
a, Đặt : \(\frac{x}{2}=\frac{y}{5}=k\)\(< =>\hept{\begin{cases}x=2k\\y=5k\end{cases}}\)
Ta có : \(x+y=27< =>2k+5k=27< =>7k=27\)
\(< =>k=\frac{27}{7}\)
Suy ra \(x=2k=\frac{54}{7};y=5k=\frac{135}{7}\)
BM
9 tháng 7 2019
\(A=\frac{99}{100}-\left(\frac{1}{1.2}+\frac{1}{2.3}+..+\frac{1}{99.100}\right)\)
\(A=\frac{99}{100}-\left(1-\frac{1}{100}\right)\)
\(A=\frac{99}{100}-\frac{99}{100}\)
\(A=\frac{99-99}{100}=0\)
9 tháng 7 2019
Bài 2
\(\left(3x+5\right).\left(2x-4\right)=0\)
\(TH1:3x+5=0\)
\(3x=-5\)
\(x=-\frac{5}{3}\)
\(TH2:2x-4=0\)
\(2x=4\)
\(x=2\)
\(\left(x^2-1\right).\left(x+3\right)=0\)
\(\Rightarrow x^2-1=0\)
\(x^2=1\)
\(\Rightarrow x=1\)
\(x+3=0\)
\(x=-3\)
\(5x^2-\frac{1}{2}x=0\)
\(\Rightarrow5x^2-\frac{x}{2}=0\)
\(\Rightarrow5x^2=\frac{5x^2}{1}=\frac{5x^2.2}{2}\)
\(10x^2-x=x.\left(10x-1\right)\)
\(\frac{x.\left(10x-1\right)}{2}=0\)
\(\frac{x.\left(10x-1\right)}{2}.2=0.2\)
\(10x-1=0\)
\(x=\frac{1}{10}=0.100\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{10}=0.100\\x=0\end{cases}}\)
\(\frac{x}{4}-\frac{1}{2}=\frac{3}{4}\)
\(\frac{x}{4}=\frac{3}{4}+\frac{1}{2}\)
\(\frac{x}{4}=\frac{5}{4}\)
\(\Rightarrow x=5\)
\(\frac{1}{8}+\frac{7}{8}:x=\frac{3}{4}\)
\(\frac{7}{8}:x=\frac{3}{4}-\frac{1}{8}\)
\(x=\frac{7}{8}:\frac{5}{8}\)
\(x=\frac{56}{40}=\frac{28}{20}=\frac{14}{10}=\frac{7}{5}\)
24 tháng 7 2016
a)\(5^x.\left(5^3\right)^2=625\)
\(5^x.5^6=5^4\)
\(5^x=5^{-2}\)
\(x=-2\)
b)\(27< 81^3:3^x< 243\)
\(3^3< \left(3^4\right)^3:3^x< 3^5\)
\(3^3< 3^{12}:3^x< 3^5\)
\(3^{12}:3^x=3^4\)
\(3^x=3^3\)
\(x=3\)
c)\(\left(5x+1\right)^2=\frac{36}{49}\)
\(\left(5x+1\right)^2=\left(\frac{6}{7}\right)^2\)
\(5x+1=\frac{6}{7}\)
\(5x=\frac{-1}{7}\)
\(x=\frac{-1}{35}\)
d)\(\left(x-\frac{2}{9}\right)^3=\left(\frac{2}{3}\right)^6\)
\(\left(x-\frac{2}{9}\right)^3=\left[\left(\frac{2}{3}\right)^2\right]^3\)
\(x-\frac{2}{9}=\frac{4}{9}\)
\(x=\frac{6}{9}=\frac{2}{3}\)
24 tháng 7 2016
\(5^x.\left(5^3\right)^2=625\)
\(\Rightarrow5^x.5^6=5^4\)
\(\Rightarrow5^{x+6}=5^4\Rightarrow x+6=4\Rightarrow x=-2\)
Đề sai rồi bạn : Phải là :
\(5^x:\left(5^3\right)^2=625\)
\(\Rightarrow5^x:5^6=5^4\)
\(\Rightarrow5^{x-6}=5^4\)
\(\Rightarrow x-6=4\Rightarrow x=10\)
Nhứng nếu đề đúng thì bạn có thể lấy KQ trên
MH
24 tháng 9 2015
a.\(\left(\frac{1}{3}-\frac{1}{2}\right)^{x-1}=\frac{1}{36}\)
\(\Rightarrow\left(-\frac{1}{6}\right)^{x-1}=\frac{1}{36}\)
\(\Rightarrow \left(-\frac{1}{6}\right)^{x-1}=\left(-\frac{1}{6}\right)^2\)
=> x-1=2
=> x=2+1
Vậy x=3.
b.\(81^{-2x}.27^x=9^5\)
\(\Rightarrow\left(3^4\right)^{-2x}.\left(3^3\right)^x=\left(3^2\right)^5\)
\(\Rightarrow3^{4.\left(-2x\right)}.3^{3x}=3^{10}\)
\(\Rightarrow3^{-8x}.3^{3x}=3^{10}\)
\(\Rightarrow3^{-5x}=3^{10}\)
=> -5x=10
=> x=10:(-5)
Vậy x=-2.
c.\(2^x+2^{x+3}=288\)
\(\Rightarrow2^x.\left(1+2^3\right)=288\)
\(\Rightarrow2^x.9=288\)
\(\Rightarrow2^x=288:9\)
\(\Rightarrow2^x=32\)
=> 2x=25
Vậy x=5.