\(\left(\dfrac{32}{243}\right)^x=\left(\dfrac{3}{2}\right)^{-1}\)

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10 tháng 10 2017

Giải:

\(\left(\dfrac{32}{243}\right)^x=\left(\dfrac{3}{2}\right)^{-1.}\)

\(\Leftrightarrow\left(\dfrac{2^5}{3^5}\right)^x=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left[\left(\dfrac{2}{3}\right)^5\right]^x=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left(\dfrac{2}{3}\right)^{5x}=\left(\dfrac{3}{2}\right)^{-1}.\)

\(\Leftrightarrow\left(\dfrac{2}{3}\right)^{5x}=\left(\dfrac{2}{3}\right)^4.\)

\(\Rightarrow5x=4\Rightarrow x=\dfrac{4}{5}.\)

Vậy.....

10 tháng 10 2017

oái, nhầm òi, kết quả là:

\(\left(\dfrac{2}{3}\right)^{5x}=\left(\dfrac{2}{3}\right)^1\Rightarrow5x=1\Rightarrow x=\dfrac{1}{5}.\)

x = 1/5 cơ, bạn tự sửa nhé :))

27 tháng 7 2017

h) \(5^x+5^{x+2}=650\)

\(\Leftrightarrow5^x+5^x.5^2=650\)

\(\Leftrightarrow5^x\left(1+25\right)=650\)

\(\Leftrightarrow5^x.26=650\)

\(\Leftrightarrow5^x=25\)

\(\Leftrightarrow x=2\)

haizzz,đăng ít thôi,chứ nhìn hoa mắt quá =.=

1 tháng 8 2017

bây định làm j ở chỗ này vậy??? có j ib ns vs nhao chớ sao ns ở đây

a: =>x=(-2/3)^5:(-2/3)^2=(-2/3)^3=-8/27

b: =>x*(-1/3)^3=(-1/3)^4

=>x=-1/3

d: =>3x-2=-3

=>3x=-1

=>x=-1/3

a: =>x-1/2=1/3

=>x=5/6

b: =>|2x-1|=x+1

\(\Leftrightarrow\left\{{}\begin{matrix}x>=-1\\\left(2x-1-x-1\right)\left(2x-1+x+1\right)=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>=-1\\\left(x-2\right)\left(3x\right)=0\end{matrix}\right.\)

hay \(x\in\left\{2;0\right\}\)

c: \(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x-\dfrac{3}{5}>\dfrac{2}{5}\\\dfrac{1}{2}x-\dfrac{3}{5}< -\dfrac{2}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x>1\\\dfrac{1}{2}x< \dfrac{1}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>2\\x< \dfrac{2}{5}\end{matrix}\right.\)

1 tháng 7 2017

a) ( x + 5 )3 = -64

x + 5 = - 4

x = - 4 - 5

x = -9

b) (2x - 3)2=9

2x - 3 = 3

2x = 3+3

2x = 6

x = 6 : 2

x = 3

e) \(\dfrac{8}{2x}=4\)

=> 4 . 2x = 8

8x =8

x = 8 : 8

x = 1

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

\(\left(\dfrac{1}{2}\right)^{2x}:\left(\dfrac{1}{2}\right)^1=\dfrac{1}{8}\)

\(\left(\dfrac{1}{2}\right)^{2x}:\dfrac{1}{2}=\dfrac{1}{8}\)

\(\left(\dfrac{1}{2}\right)^{2x}=\dfrac{1}{8}.\dfrac{1}{2}\)

\(\left(\dfrac{1}{2}\right)^{2x}=\dfrac{1}{16}\)

\(\left(\dfrac{1}{2}\right)^{2x}=\left(\dfrac{1}{2}\right)^{2.2}\)

=> x = 2

h) \(\left(\dfrac{1}{2}\right)^2.x=\left(\dfrac{1}{2}\right)^5\)

\(\dfrac{1}{4}.x=\dfrac{1}{32}\)

x = \(\dfrac{1}{32}:\dfrac{1}{4}\)

x = \(\dfrac{1}{8}\)

i) \(\left(\dfrac{-1}{3}\right)x=\dfrac{1}{81}\)

\(x=\dfrac{1}{81}:\left(\dfrac{-1}{3}\right)\)

\(x=\dfrac{-1}{27}\)

2 tháng 7 2017

a) (x + 5)3 = -64

=> (x + 5)3 = (-4)3

x + 5 = -4

x = -4 - 5

x = -9

b) (2x - 3)2 = 9

=> (2x - 3)2 = (\(\pm\)3)2

=> 2x - 3 = 3 hoặc 2x - 3 = -3

*2x - 3 = 3

2x = 3 + 3

2x = 9

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

*2x - 3 = -3

2x = -3 + 3

2x = 0

x = 0 : 2

x = 0

Vậy x \(\in\left\{\dfrac{9}{2};0\right\}\)

c) \(\dfrac{x}{\dfrac{4}{2}}=\dfrac{4}{\dfrac{x}{2}}\)

=> \(x.\dfrac{x}{2}=4.\dfrac{4}{2}\)

\(\dfrac{x}{2}=8\)

x = 8 : 2

x = 4

d) \(\dfrac{-32}{\left(-2\right)^n}=4\)

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

=> (-2)n . (-2)2= (-2)5

(-2)n = (-2)5 : (-2)2

(-2)n = (-2)3

Vậy n = 3

e) \(\dfrac{8}{2x}=4\)

=> 2x . 4 = 8

2x = 8 : 4

2x = 2

x = 1

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

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

2x - 1 = 3

2x = 3 + 1

2x = 4

x = 4 : 2

x = 2

h) \(\left(\dfrac{1}{2}\right)^2.x=\left(\dfrac{1}{2}\right)^5\)

\(x=\left(\dfrac{1}{2}\right)^5:\left(\dfrac{1}{2}\right)^2\)

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

\(x=\dfrac{1}{8}\)

i) \(\left(\dfrac{-1}{3}\right)x=\dfrac{1}{81}\)

\(x=\dfrac{1}{81}:\left(\dfrac{-1}{3}\right)\)

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

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

\(x=\dfrac{-1}{27}\).

21 tháng 6 2017

1)

a) \(0,25^x\cdot12^x=243\)

\(\Leftrightarrow\left(0,25\cdot12\right)^x=3^5\)

\(\Leftrightarrow3^x=3^5\)

\(\Leftrightarrow x=5\)

Vậy \(x=5\)

b) \(38^y:19^y=512\)

\(\Leftrightarrow2y\cdot y=512\)

\(\Leftrightarrow2y^2=512\)

\(\Leftrightarrow y^2=256\)

\(\Leftrightarrow\left[{}\begin{matrix}y=16\\y=-16\end{matrix}\right.\)

Vậy \(y_1=-16;y_2=16\)

2)

a) \(3^x+3^{x+2}=2430\)

\(\Leftrightarrow\left(1+3^2\right)\cdot3^x=2430\)

\(\Leftrightarrow\left(1+9\right)\cdot3^x=2430\)

\(\Leftrightarrow10\cdot3^x=2430\)

\(\Leftrightarrow3^x=243\)

\(\Leftrightarrow3^x=3^5\)

\(\Leftrightarrow x=5\)

Vậy \(x=5\)

b) \(2^{x+3}-2^x=224\)

\(\Leftrightarrow\left(2^3-1\right)\cdot2^x=224\)

\(\Leftrightarrow\left(8-1\right)\cdot2^x=224\)

\(\Leftrightarrow7\cdot2^x=224\)

\(\Leftrightarrow2^x=32\)

\(\Leftrightarrow2^x=2^5\)

\(\Leftrightarrow x=5\)

Vậy \(x=5\)

3)

a) \(\left(x-\dfrac{1}{4}\right)^2=\dfrac{4}{9}\)

\(\Leftrightarrow x-\dfrac{1}{4}=\pm\dfrac{2}{3}\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{11}{12}\\x=-\dfrac{5}{12}\end{matrix}\right.\)

Vậy \(x_1=\dfrac{11}{12};x_2=-\dfrac{5}{12}\)

b) \(\left(x+0,7\right)^3=-27\)

\(\Leftrightarrow\left(x+\dfrac{3}{10}\right)^3=\left(-3\right)^3\)

\(\Leftrightarrow x+\dfrac{3}{10}=-3\)

\(\Leftrightarrow x=-3-\dfrac{3}{10}\)

\(\Leftrightarrow x=-\dfrac{37}{10}\)

Vậy \(x=-\dfrac{37}{10}\)

4)

a) \(\left(\dfrac{2}{5}-3x\right)^2=\dfrac{9}{25}\)

\(\Leftrightarrow\dfrac{2}{5}-3x=\pm\dfrac{3}{5}\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{5}-3x=\dfrac{3}{5}\\\dfrac{2}{5}-3x=-\dfrac{3}{5}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3x=-\dfrac{1}{5}\\3x=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{15}\\x=\dfrac{1}{3}\end{matrix}\right.\)

Vậy \(x_1=-\dfrac{1}{15};x_2=\dfrac{1}{3}\)

b) \(\left(\dfrac{2}{3}x-\dfrac{1}{3}\right)^5=\dfrac{1}{243}\)

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

\(\Leftrightarrow2x-1=1\)

\(\Leftrightarrow2x=1+1\)

\(\Leftrightarrow2x=2\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

21 tháng 6 2017

1. a) \(0,25^x.12^x=243\)

\(\Rightarrow\left(0,25.12\right)^x=243\)

\(\Rightarrow3^x=3^5\)

\(\Rightarrow x=5\)

Vậy \(x=5.\)

b) \(38^y:19^y=512\)

\(\Rightarrow\left(38:19\right)^y=512\)

\(\Rightarrow2^y=2^9\)

\(\Rightarrow y=9\)

Vậy \(y=9.\)

2) a) \(3^x+3^{x+2}=2430\)

\(\Rightarrow3^x\left(1+9\right)=2430\)

\(\Rightarrow3^x=243=3^5\)

\(\Rightarrow x=5\)

Vậy x=5.

b) \(2^{x+3}-2^x=224\)

\(\Rightarrow2^x\left(8-1\right)=224\)

\(\Rightarrow2^x=32=2^5\)

\(\Rightarrow x=5\)

Vậy x=5.

Bài 3: dễ tự làm.

16 tháng 9 2017

cái này mà bạn ko biết làm á, bấm máy tính tạch tạch mấy phát là ra mà

17 tháng 9 2017

lười làm nên nhờ mấy bạn giải dùm

21 tháng 3 2018

Câu hỏi của chíp chíp - Toán lớp 7 | Học trực tuyến Full dễ ok??

OK???????

21 tháng 3 2018

Trừ câu F ra thì dệ hết

a: TH1: x>=0

=>x+x=1/3

=>x=1/6(nhận)

TH2: x<0

Pt sẽ là -x+x=1/3

=>0=1/3(loại)

b: \(\Leftrightarrow\left\{{}\begin{matrix}x>=0\\x^2-x-2=0\end{matrix}\right.\Leftrightarrow x=2\)

c: \(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{1}{x-3}+\dfrac{1}{x-3}-\dfrac{1}{x-8}+\dfrac{1}{x-8}-\dfrac{1}{x-20}-\dfrac{1}{x-20}=\dfrac{-3}{4}\)

\(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{2}{x-20}=\dfrac{-3}{4}\)

\(\Leftrightarrow\dfrac{x-20-2x+2}{\left(x-1\right)\left(x-20\right)}=\dfrac{-3}{4}\)

\(\Leftrightarrow-3\left(x^2-21x+20\right)=4\left(-x-18\right)\)

\(\Leftrightarrow3x^2-63x+60=4x+72\)

=>3x^2-67x-12=0

hay \(x\in\left\{22.51;-0.18\right\}\)

23 tháng 10 2017

\(\left(\dfrac{1}{3}\right)^x+\left(\dfrac{1}{3}\right)^{x+2}=\dfrac{10}{243}\)

\(\left(\dfrac{1}{3}\right)^x+\left(\dfrac{1}{3}\right)^x.\left(\dfrac{1}{3}\right)^2=\dfrac{10}{243}\)

\(\left(\dfrac{1}{3}\right)^x.\left[1+\left(\dfrac{1}{3}\right)^2\right]=\dfrac{10}{243}\)

\(\left(\dfrac{1}{3}\right)^x.\dfrac{10}{9}=\dfrac{10}{243}\)

\(\left(\dfrac{1}{3}\right)^x=\dfrac{10}{243}:\dfrac{10}{9}\)

\(\left(\dfrac{1}{3}\right)^x=\dfrac{1}{27}\)

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

\(\Rightarrow x=3\)