2^-1.2^x+4.2^x=9.2^5

0,5.2^x+4.2^x=288

2^x.(4+0,5)=288

2^x.4,5=288

2^x=288:4,5

2^x=64

2^x=2^6

=) x=6

a, \(3^{-2}.3^4.3^x=3^7\)

\(\Rightarrow3^{-2+4+x}=3^7\)

\(\Rightarrow3^{2+x}=3^7\)

Vì \(3\ne\pm1;3\ne0\) nên \(2+x=7\Rightarrow x=5\)

b, \(2^{-1}.2^x+4.2^x=9.2^5\)

\(\Rightarrow2^x\left(2^{-1}+4\right)=288\)

\(\Rightarrow2^x.4,5=288\Rightarrow2^x=64=2^6\)

Vì \(2\ne\pm1;2\ne0\) nên \(x=6\)

Chúc bạn học tốt!!!

a, 3600: [ ( 5x + 35 ) : x ] = 50

<=> ( 5x + 35 ) : x = 72

<=> 5x + 35 = 72x

<=> 72x - 5x = 35

<=> 67x = 35

<=> x = 35/67

b, 2^n-1 + 4 . 2ⁿ = 9 . 2⁵ 

<=> 2ⁿ : 2 + 4 . 2ⁿ  = 9 . 2⁵ 

<=> 2ⁿ . 1/2 + 4 . 2ⁿ  = 9 . 2⁵ 

<=> 2ⁿ . ( 1/2 + 4 ) = 9 . 2⁵   

<=> 2ⁿ . 9/2 = 9 . 2⁵ 

<=> 2ⁿ : 2⁵ = 9 : 9/2

<=> 2^{n - 5} = 2¹ 

<=> n - 5 = 1

<=> n = 6

a) 2^-1.2^x + 4.2^x = 9.2⁵

=> 2^x-1 + 4.2.2^x-1 = 9.2⁵

=> 2^x-1 + 8.2^x-1 = 9.2⁵

=> 2^x-1.(1 + 8) = 9.2⁵

=> 2^x-1.9 = 9.2⁵

=> x - 1 = 5

=> x = 5 + 1 = 6

Vậy x = 6

b) (7x + 2)^-1 = \(\frac{1}{9}\)

=> 7x + 2 = 9

=> 7x = 9 - 2

=> 7x = 7

=> x = 7 : 7 = 1

Vậy x = 1

a)     2^(-1) . 2^x + 4 . 2^x = 9 . 2^5

=>    1/2 . 2^x + 4 . 2^x     = 9 . 32

=>    2^x . (1/2 + 4)           = 288

=>   2^x . 9/2 = 288 

=> 2^x = 288 : 9/2

=> 2^x = 64

      2^x = 2^6

=> x = 6

b) (7x + 2)^(-1) = 1/9

=> 1 phần 7x + 2  = 1/9

=> 7x + 2 = 9

=> 7x = 9 - 2 

=> 7x = 7

=> x = 7 : 7

=> x = 1

\(\frac{1}{2}.2^x+4.2^x=9.2^5\)

\(\Rightarrow\)2^x(\(\frac{1}{2}+4\))=9.2⁵

\(\Rightarrow\)\(\frac{9}{2}.2^x=9.2^5\)

\(\Rightarrow9.2^{x-1}=9.2^5\)

\(\Rightarrow2^{x-1}=2^5\)

\(\Rightarrow\)x-1=5

\(\Rightarrow\)x=6(tm)

Vậy x=6