\(\left(\dfrac{1}{2}\right)^x+\left(\dfrac{1}{2}\right)^{x+3}=\dfrac{9}{256}\)

tì...">

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AH
Akai Haruma
Giáo viên
30 tháng 11 2018

Lời giải:
\(\left(\frac{1}{2}\right)^x+\left(\frac{1}{2}\right)^{x+3}=\frac{9}{256}\)

\(\Leftrightarrow \left(\frac{1}{2}\right)^x+\left(\frac{1}{2}\right)^x.\left(\frac{1}{2}\right)^3=\frac{9}{256}\)

\(\Leftrightarrow \left(\frac{1}{2}\right)^x.(1+\frac{1}{8})=\frac{9}{256}\Rightarrow \left(\frac{1}{2}\right)^x=\frac{1}{32}=\left(\frac{1}{2}\right)^5\)

\(\Rightarrow x=5\)

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: \(\Leftrightarrow\left(\dfrac{12}{25}\right)^x=\dfrac{9}{25}-\dfrac{81}{625}=\dfrac{144}{625}\)

=>x=2

b: =>3x-1=-4

=>3x=-3

hay x=-1

 

17 tháng 5 2017

\(\dfrac{-1}{4}x+\dfrac{2}{3}=\dfrac{5}{9}\)\(\Rightarrow\)\(\dfrac{-1}{4}x=\dfrac{5}{9}-\dfrac{2}{3}\)=\(\dfrac{-1}{9}\)

\(\Rightarrow\) x = \(\dfrac{-1}{9}:\dfrac{-1}{4}\)=\(\dfrac{4}{9}\).

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

\(\Rightarrow\)x=\(\dfrac{3}{5}:\left(\dfrac{3}{5}\right)^3=\left(\dfrac{3}{5}\right)^{-2}\)= \(2\dfrac{7}{9}\)

\(\left|x\right|\) + \(\dfrac{1}{5}=2-\left(\dfrac{2}{3}-\dfrac{3}{4}\right)\)=2 - \(\dfrac{-1}{12}\)=2\(\dfrac{1}{12}\)

\(\Rightarrow\)\(\left|x\right|\)=\(2\dfrac{1}{12}\)-\(\dfrac{1}{5}\)=\(1\dfrac{53}{60}\)

\(\Rightarrow\)x=\(\left[{}\begin{matrix}1\dfrac{53}{60}\\-1\dfrac{53}{60}\end{matrix}\right.\)

\(\left(\dfrac{-3}{4}\right)^x=\dfrac{81}{256}\)=\(\dfrac{(-3)^4}{4^4}\)=\(\left(\dfrac{-3}{4}\right)^4\)

\(\Rightarrow\) x = 4

17 tháng 5 2017

14 Mẹo Vặt Sáng Tạo Dành Cho Học Sinh - YouTube

thử xem mẹo thứ 5 đi chứ theo mk đây là bài toán dễ lớp 6

30 tháng 10 2022

a: \(\Leftrightarrow2x-3=x\)

=>x=3

b: \(\Leftrightarrow2^x\cdot\dfrac{1}{2}+\dfrac{5}{4}\cdot2^x=\dfrac{7}{32}\)

=>2^x=1/8

=>x=-3

c: =>2x+7=-4

=>2x=-11

=>x=-11/2

d: =>(4x-3)^2*(4x-4)(4x-2)=0

hay \(x\in\left\{\dfrac{3}{4};1;\dfrac{1}{2}\right\}\)

1: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{8}\right)^6\)

\(\Leftrightarrow\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{18}\)

=>4x=18

hay x=9/2

2: \(\left(\dfrac{1}{16}\right)^x=\left(\dfrac{1}{8}\right)^{36}\)

\(\Leftrightarrow\left(\dfrac{1}{2}\right)^{4x}=\left(\dfrac{1}{2}\right)^{108}\)

=>4x=108

hay x=27

3: \(\left(\dfrac{1}{81}\right)^x=\left(\dfrac{1}{27}\right)^4\)

\(\Leftrightarrow\left(\dfrac{1}{3}\right)^{4x}=\left(\dfrac{1}{3}\right)^{12}\)

=>4x=12

hay x=3

27 tháng 11 2017

a)

\(\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|=-\dfrac{1}{4}-y\\ \Rightarrow\left\{{}\begin{matrix}\dfrac{1}{2}-\dfrac{1}{3}+x=-\dfrac{1}{4}-y\\\dfrac{1}{2}-\dfrac{1}{3}+x=\dfrac{1}{4}+y\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+y=-\dfrac{5}{12}\\x-y=\dfrac{1}{12}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{6}\\y=-\dfrac{1}{4}\end{matrix}\right.\)

b)\(\left|x-y\right|+\left|y+\dfrac{9}{25}\right|=0\)

ta thấy : \(\left|x-y\right|\ge0\\ \left|y+\dfrac{9}{25}\right|\ge0\)\(\Rightarrow\left|x-y\right|+\left|y+\dfrac{9}{25}\right|\ge0\)

đẳng thửc xảy ra khi : \(\left\{{}\begin{matrix}x-y=0\\y+\dfrac{9}{25}=0\end{matrix}\right.\Rightarrow x=y=-\dfrac{9}{25}\)

vậy \(\left(x;y\right)=\left(-\dfrac{9}{25};-\dfrac{9}{25}\right)\)

27 tháng 11 2017

c) \(\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}=0\)

ta thấy \(\left(\dfrac{1}{2}x-5\right)^{20}\:và\:\left(y^2-\dfrac{1}{4}\right)^{10}\) là các lũy thừa có số mũ chẵn

\(\Rightarrow\:\)\(\left(\dfrac{1}{2}x-5\right)^{20}\ge0\\ \left(y^2-\dfrac{1}{4}\right)^{10}\ge0\)\(\Rightarrow\left(\dfrac{1}{2}x-5\right)^{20}+\left(y^2-\dfrac{1}{4}\right)^{10}\ge0\)

đẳng thức xảy ra khi \(\left\{{}\begin{matrix}\dfrac{1}{2}x-5=0\\y^2-\dfrac{1}{4}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=10\\\left[{}\begin{matrix}y=-\dfrac{1}{2}\\y=\dfrac{1}{2}\end{matrix}\right.\end{matrix}\right.\)

vậy cặp số x,y cần tìm là \(\left(10;\dfrac{1}{2}\right)\:hoặc\:\left(10;-\dfrac{1}{2}\right)\)

d)

\(\left|x\left(x^2-\dfrac{5}{4}\right)\right|=x\\ \Leftrightarrow x\left(x^2-\dfrac{5}{4}\right)=x\left(vì\:x\ge0\right)\\ \Leftrightarrow x\left(x^2-\dfrac{9}{4}\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^2-\dfrac{9}{4}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{3}{2}\end{matrix}\right.\end{matrix}\right.\)

vậy x cần tìm là \(-\dfrac{3}{2};0;\dfrac{3}{2}\)

e)\(x^2+\left(y-\dfrac{1}{10}\right)^4=0\)

ta thấy: \(x^2\ge0;\left(y-\dfrac{1}{10}\right)^4\ge0\)

\(\Rightarrow x^2+\left(y-\dfrac{1}{10}\right)^4\ge0\)

đẳng thức xảy ra khi: \(\left\{{}\begin{matrix}x=0\\y=\dfrac{1}{10}\end{matrix}\right.\)

vậy cặp số cần tìm là \(0;\dfrac{1}{10}\)

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

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

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

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

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

9 tháng 10 2017

\((\dfrac{1}{2})^{15}\times(\dfrac{1}{2})^{20}=(\dfrac{1}{2})^{15+20}=(\dfrac{1}{2})^{35}\) \([(\dfrac{1}{3})^2]^{25}\div(\dfrac{1}{3})^{30}=(\dfrac{1}{3})^{50}\div(\dfrac{1}{3})^{30}=(\dfrac{1}{3})^{50-30}=(\dfrac{1}{3})^{20}\) \((\dfrac{1}{16})^3\div(\dfrac{1}{8})^2=[(\dfrac{1}{2})^4]^3\div[(\dfrac{1}{2})^3]^2=(\dfrac{1}{2})^{12}\div(\dfrac{1}{2})^6=(\dfrac{1}{2})^{12-6}=(\dfrac{1}{2})^6\) (x^3)^2 : ( x^2)^3= x^6 :x^6=1

23 tháng 11 2018

\(\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{2}\right)^{20}=\left(\dfrac{1}{2}\right)^{15+20}=\left(\dfrac{1}{2}\right)^{35}\)

\(\left(\dfrac{1}{9}\right)^{25}:\left(\dfrac{1}{3}\right)^{30}=\left[\left(\dfrac{1}{3}\right)^2\right]^{25}:\left(\dfrac{1}{3}\right)^{30}=\left(\dfrac{1}{3}\right)^{50}:\left(\dfrac{1}{3}\right)^{30}=\left(\dfrac{1}{3}\right)^{50-30}=\left(\dfrac{1}{30}\right)^{20}\)\(\left(\dfrac{1}{16}\right)^3:\left(\dfrac{1}{8}\right)^2=\left[\left(\dfrac{1}{2}\right)^4\right]^3:\left[\left(\dfrac{1}{2}\right)^3\right]^2=\left(\dfrac{1}{2}\right)^{12}:\left(\dfrac{1}{2}\right)^6=\left(\dfrac{1}{2}\right)^{12-6}=\left(\dfrac{1}{2}\right)^6\)

\(\left(x^3\right)^2:\left(x^2\right)^3=x^6:x^6=x^0=1\)