Ta có :

\(8< 2^x\le2^9.2^{-5}\)(1)

Xét :

\(2^9.2^{-5}=2^9.\frac{1}{2^5}=2^4\)(2)

Thay (2) vào (1) ta có :

\(\Rightarrow2^3< 2^x\le2^4\)

\(\Rightarrow2^x=2^4\)

\(\Rightarrow x=4\)

a)x ∈ ∅

b) x=3

\(a,\Rightarrow2^3< 2^x\le2^4\Rightarrow x=4\\ b,\Rightarrow3^3< 3^{12}:3^x< 3^5\\ \Rightarrow3^3< 3^{12-x}< 3^5\\ \Rightarrow12-x=4\Rightarrow x=8\)

a) \(8< 2^x\le2^9.2^{-5}\)

\(\Leftrightarrow2^3< x\le2^{9-5}\)

\(\Leftrightarrow2^3< 2^x\le2^4\)

\(\Leftrightarrow3< x\le4\Leftrightarrow x=4\)

b) \(27< 81^3:3^x< 243\)

\(\Leftrightarrow3^2< \left(3^4\right)^3:3^x< 3^5\)

\(\Leftrightarrow3^2< 3^{12}:3^x< 3^5\)

\(\Leftrightarrow3^2< 3^{12-x}< 3^5\)

\(\Leftrightarrow2< 12-x< 5\)

\(\Leftrightarrow\hept{\begin{cases}x=8\\x=9\end{cases}}\)

a)\(32^{-n}\cdot16^n=2048\)

\(\left(2^5\right)^{-n}\cdot\left(2^4\right)^n\)=2048

\(2^{-5n}\cdot2^{4n}\)=\(2^{11}\)

\(2^{-5n+4n}=2^{11}\)

\(2^{-x}=2^{11}\)

\(\Rightarrow x=-11\)

b)\(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)

\(\frac{1}{2}\cdot2^n+4\cdot2^n=288\)

\(2^n\left(\frac{1}{2}+4\right)=288\)

\(2^n\cdot\frac{9}{2}=288\)

\(2^n=288:\frac{9}{2}\)

\(2^n=64\)

\(2^n=2^6\)

\(\Rightarrow n=6\)

a) 32^-n . 16ⁿ = 2048

\(\frac{1}{32n}\) . 16ⁿ = 2048

\(\frac{1}{2^n.16^n}\) . 16ⁿ = 2048

\(\frac{1}{2^n}\) = 2048

2^-n = 2048

2^-n = 2¹¹

\(\Rightarrow\) -n = 11

\(\Rightarrow\) n = -11

Vậy n = -11

Bài 1:

a) \(\dfrac{9}{20}-\dfrac{8}{15}\times\dfrac{5}{12}\)

\(=\dfrac{9}{20}-\dfrac{2}{9}\)

\(=\dfrac{41}{180}\)

b) \(\dfrac{2}{3}\div\dfrac{4}{5}\div\dfrac{7}{12}\)

\(=\dfrac{2}{3}\times\dfrac{5}{4}\times\dfrac{12}{7}\)

\(=\dfrac{5}{6}\times\dfrac{12}{7}\)

\(=\dfrac{10}{7}\)

c) \(\dfrac{7}{9}\times\dfrac{1}{3}+\dfrac{7}{9}\times\dfrac{2}{3}\)

\(=\dfrac{7}{9}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)

\(=\dfrac{7}{9}\times1\)

\(=\dfrac{7}{9}\)

Bài 2:

a) \(2\times\left(x-1\right)=4026\)

\(\left(x-1\right)=4026\div2\)

\(x-1=2013\)

\(x=2014\)

Vậy: \(x=2014\)

b) \(x\times3,7+6,3\times x=320\)

\(x\times\left(3,7+6,3\right)=320\)

\(x\times10=320\)

\(x=320\div10\)

\(x=32\)

Vậy: \(x=32\)

c) \(0,25\times3< 3< 1,02\)

\(\Leftrightarrow0,75< 3< 1,02\) ( S )

=> \(0,75< 1,02< 3\)

\(\Leftrightarrow2^n\left(\frac{1}{2}+4\right)=9\cdot2^5\Leftrightarrow2^n\cdot\frac{9}{2}=9\cdot2^5\Leftrightarrow2^n=2^6\Leftrightarrow n=6\)

a,\(8< 2^x\le2^9.2^{-5}\)

\(2^3< 2^x\le2^4\)

\(\Rightarrow x=4\)

b, \(27< 81^3.3^x< 243\)

\(3^3< 3^{12-x}< 3^5\)

\(\Rightarrow3< 12-x< 5\)

12-x=4

x=8

c,\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^3.\left(\frac{2}{5}\right)^2\)

\(\left(\frac{2}{5}\right)^x>\left(\frac{2}{5}\right)^5\)

\(\Rightarrow x>5\)

x=6;7;8........

tìm x, biết:

(5x+1)^2=36/49

a) 84

b) -300

c) 1700

a) = 10 . ( 7.8 )

= 10 . 56 

= 560 

b) 

= 9.2.7.5

= ( 9.7 ) . ( 2.5 )

= 63 . 10 

= 630 

b) 7.x=42

x = 42 : 7 

x = 6

c) 180 : x = -12

x = 180 : ( -12 )

x = -15

b,84  c,-300  d,1700

a,=560  b,=630  

b)(-12).(-7)=84

c)15.(-20)=-300

D)34.50=1700

a)7.2.5.8

=2.5.7.8

=10.56

=560

b)9.2.(-7).(-5)

=2.(-5).9.(-7)

=(-10).(-63)

=630

b)7.x=42

      X=42:7

      X=6

c)180:x=-12

           x=180:(-12)

           x=-15