\(\left(\dfrac{1}{3}\right)^{2n-1}=243\)
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22 tháng 7 2017

a,\(\left(\dfrac{1}{3}\right)^{2n-1}=243\)

\(\Rightarrow\left(\dfrac{1}{3}\right)^{2n-1}=\left(\dfrac{1}{3}\right)^{-5}\)

\(\dfrac{1}{3}\ne\pm1;\dfrac{1}{3}\ne0\) nên

\(2n-1=-5\Rightarrow2n=-4\Rightarrow n=-2\)

Vậy........

b, \(\left(0,125\right)^{n+1}=64\)

\(\Rightarrow\left(\dfrac{1}{8}\right)^{n+1}=\left(\dfrac{1}{8}\right)^{-2}\)

\(\dfrac{1}{8}\ne\pm1;\dfrac{1}{8}\ne0\) nên

\(n+1=-2\Rightarrow n=-3\)

Vậy..........

Chúc bạn học tốt!!!

22 tháng 7 2017

a) Ta có: \(\left(\dfrac{1}{3}\right)^{2n-1}=243\Rightarrow\left(3^{-1}\right)^{2n-1}=3^5\)

\(\Rightarrow3^{-2n+1}=3^5\)

Suy ra: \(-2n+1=5\Rightarrow-2n=4\Rightarrow n=-2\)

b) \(\left(0,125\right)^{n+1}=64\Rightarrow\left(\dfrac{1}{8}\right)^{n+1}=8^2\)

\(\Rightarrow\left(8^{-1}\right)^{n+1}=8^2\)

\(\Rightarrow8^{-n-1}=8^2\)

Suy ra: \(-n-1=2\Rightarrow n=-3\)

Hok tốt

30 tháng 8 2017

a)\(3,8:\left(2x\right)=\dfrac{1}{4}:2\dfrac{2}{3}\)

\(2x=3,8:\dfrac{3}{32}\)

\(x=\dfrac{608}{15}:2\)

\(x=\dfrac{304}{15}\)

b)\(\left(0,25x\right):3=\dfrac{5}{6}:0,125\)

\(0,25x=\dfrac{20}{3}\times3\)

\(x=20:0,25\)

\(x=80\)

c) \(0,01:2,5=\left(0,75\times x\right):0,75\)

\(0,004=0,75\times x:0,75\)

\(0,004=x\times0,75:0,75\)

\(0,004=x\times1\)

\(0,004=x\)

\(\Rightarrow x=0,004\)

d)\(1\dfrac{1}{3}:0,8=\dfrac{2}{3}:\left(0,1x\right)\)

\(\dfrac{5}{3}=\dfrac{2}{3}:0,1\times x\)

\(\dfrac{5}{3}=\dfrac{20}{3}\times x\)

\(\Rightarrow x=\dfrac{20}{3}:\dfrac{5}{3}\)

\(x=4\)

10 tháng 6 2017

a) \(x=20\dfrac{4}{15}.\)

b) \(x=80\)

c) \(x=0,004\)

d) \(x=4.\)

9 tháng 6 2017

Sau khi thực hiện phép tính ta được kết quả các giá trị:

\(A=\dfrac{1}{3}\) \(B=-5\dfrac{5}{12}\) \(C=-0,22\)

Sắp xếp: \(-5\dfrac{5}{12}< -0,22< \dfrac{1}{3}\) tức là \(B< C< A\)

28 tháng 8 2017

Khi tính xong giá trị biểu thức A , B và C ta được kết quả như sau :

\(A=\dfrac{1}{3}\) ; \(B=-5\dfrac{5}{12}\); \(C=-0,22\)

Sắp xếp : \(B< C< A\)\(\left(-5\dfrac{5}{12}< -0,22< \dfrac{1}{3}\right)\)

23 tháng 9 2017

a) \(\left(5x+1\right)^2=\dfrac{36}{49}\)

\(\left(5x+1\right)^2=\left(\pm\dfrac{6}{9}\right)\)\(^2\)

\(5x+1=\pm\dfrac{6}{9}\)

+) \(5x+1=\dfrac{6}{9}\)

\(5x=\dfrac{6}{9}-1=\dfrac{6}{9}-\dfrac{9}{9}\)

\(5x=\dfrac{-5}{9}\)

\(x=\dfrac{-5}{9}:5=\dfrac{-1}{45}\)

+) \(5x+1=\dfrac{-6}{9}\)

\(5x=\dfrac{-6}{9}-1=\dfrac{-6}{9}-\dfrac{9}{9}\)

\(5x=\dfrac{-5}{3}\)

\(x=\dfrac{-5}{3}:5=\dfrac{-5}{15}\)

vậy \(x\in\left\{\dfrac{-5}{15};\dfrac{-1}{45}\right\}\)

18 tháng 4 2017

\(P=\left(0,5-\dfrac{3}{5}\right):\left(-3\right)+\dfrac{1}{3}-\left(-\dfrac{1}{6}\right):\left(-2\right)\)

\(=\left(-\dfrac{1}{2}-\dfrac{3}{5}\right):\left(-3\right)+\dfrac{1}{3}-\left(-\dfrac{1}{6}\right).\left(-\dfrac{1}{2}\right)\)

\(=\left(\dfrac{-5-6}{10}\right):\left(-3\right)+\dfrac{1}{3}-\dfrac{1}{12}\)

\(=-\dfrac{11}{10}:\left(-3\right)+\dfrac{1}{4}\)

\(=-\dfrac{11}{10}.\left(-\dfrac{1}{3}\right)+\dfrac{1}{4}=\dfrac{11}{30}+\dfrac{1}{4}=\dfrac{37}{60}\)

Vậy \(P=\dfrac{37}{60}\)

\(Q=\left(\dfrac{2}{25}-1,008\right):\dfrac{4}{7}:\left[\left(3\dfrac{1}{4}-6\dfrac{5}{9}\right):2\dfrac{2}{17}\right]\)

\(=\left(\dfrac{2}{25}-\dfrac{126}{125}\right):\dfrac{4}{7}:\left[\left(\dfrac{13}{4}-\dfrac{59}{9}\right).\dfrac{36}{17}\right]\)

\(=-\dfrac{116}{125}.\dfrac{7}{4}:\left(-\dfrac{119}{36}.\dfrac{36}{17}\right)\)

\(=\dfrac{-29.7}{125}:\left(-7\right)=\dfrac{29}{125}\)

Vậy \(Q=\dfrac{29}{125}\)

14 tháng 7 2017

a,

\(\left(4x-\dfrac{1}{3}\right)^6=1\\ \Rightarrow\left[{}\begin{matrix}4x-\dfrac{1}{3}=1\\4x-\dfrac{1}{3}=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}4x=\dfrac{4}{3}\\4x=\dfrac{-2}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=\dfrac{-1}{6}\end{matrix}\right.\)

b,

\(\left(5x-\dfrac{2}{3}\right)^2=0\\ \Rightarrow5x-\dfrac{2}{3}=0\\ 5x=\dfrac{2}{3}\\ x=\dfrac{2}{15}\)

c,

\(\left(\dfrac{1}{3}x-\dfrac{1}{2}\right)^3=-8\\ \Rightarrow\dfrac{1}{3}x-\dfrac{1}{2}=-2\\ \dfrac{1}{3}x=\dfrac{-3}{2}\\ x=\dfrac{-9}{2}\)

d,

\(\dfrac{81}{3^n}=3\\ \Leftrightarrow3^4:3^n=3^1\\\Leftrightarrow3^{4-n}=3^1 \\ \Rightarrow n=3\)

e,

\(\dfrac{\left(-2\right)^x}{64}=-2\\ \Leftrightarrow\left(-2\right)^x:\left(-2\right)^6=\left(-2\right)^1\\ \Leftrightarrow\left(-2\right)^{x-6}=\left(-2\right)^1\\ \Rightarrow x=7\)

f,

\(\left(-20\right)^n:10^n=16\\ \left[\left(-20\right):10\right]^n=16\\ \left(-2\right)^n=\left(-2\right)^4\\ \Rightarrow n=4\)

14 tháng 7 2017

Bài 1:

a) \(\left(4x-\dfrac{1}{3}\right)^6=1\)

\(\Rightarrow4x-\dfrac{1}{3}=1\)

\(4x=1+\dfrac{1}{3}\)

\(4x=\dfrac{4}{3}\)

\(x=\dfrac{4}{3}:4\)

\(x=\dfrac{1}{3}\)

b) \(\left(5x-\dfrac{2}{3}\right)^2=0\)

\(\Rightarrow5x-\dfrac{2}{3}=0\)

\(5x=\dfrac{2}{3}\)

\(x=\dfrac{2}{3}:5\)

\(x=\dfrac{2}{15}\)

c) \(\left(\dfrac{1}{3}x-\dfrac{1}{2}\right)^3=-8\)

\(\Rightarrow\left(\dfrac{1}{3}x-\dfrac{1}{2}\right)^3=\left(-2\right)^3\)

\(\dfrac{1}{3}x-\dfrac{1}{2}=-2\)

\(\dfrac{1}{3}x=-2+\dfrac{1}{2}\)

\(\dfrac{1}{3}x=\dfrac{-3}{2}\)

\(x=\dfrac{-3}{2}:\dfrac{1}{3}\)

\(x=\dfrac{-9}{2}\)

d) \(\dfrac{81}{3^n}=3\)

\(\Rightarrow\dfrac{3^4}{3^n}=3\)

\(\Rightarrow3^n.3=3^4\)

\(3^{n+1}=3^4\)

n + 1 = 4

n = 4 - 1

n = 3

e) \(\dfrac{\left(-2\right)^x}{64}=-2\)

\(\Rightarrow\dfrac{\left(-2\right)^x}{\left(-2\right)^6}=-2\)

\(\Rightarrow\left(-2\right)^x=\left(-2\right)^6.\left(-2\right)\)

\(\left(-2\right)^x=\left(-2\right)^7\)

x = 7

f) (-20)n : 10n = 16

(-20 : 10)n = 16

(-2)n = 16

(-2)n = (-2)4

n = 4.

15 tháng 8 2017

Nhiều quá bạn ơi ( Hhôm nào cũng thấy đăng 6,7 câu )

15 tháng 8 2017

giúp người đi bạn

a: =>5x+1=6/7 hoặc 5x+1=-6/7

=>5x=-1/7 hoặc 5x=-13/7

=>x=-1/35 hoặc x=-13/35

b: =>x-2/9=4/9

=>x=6/9=2/3

c: =>8x+1=5

=>8x=4

hay x=1/2

10 tháng 6 2017

\(A=\left(3,1-2,5\right)-\left(-2,5+3,1\right)\)

\(A=3,1-2,5+2,5-3,1\)

\(A=\left(3,1-3,1\right)-\left(2,5-2,5\right)\)

\(A=0-0\)

\(A=0\)

10 tháng 6 2017

\(B=\left(5,3-2,8\right)-\left(4+5,3\right)\)

\(B=5,3-2,8-4-5,3\)

\(B=\left(5,3-5,3\right)-\left(2,8+4\right)\\ B=0-6,8\\ B=-6,8\)