2^-1.2ⁿ+4.2ⁿ=9.2⁵

=>2^n-1+2².2ⁿ=9.2⁵

=>2^n-1+2ⁿ⁺²=9.2⁵

=>2^n-1.(2³+1)=9.2⁵

=>2^n-1.9=9.2⁵

=>2^n-1=2⁵

=>n-1=5=>n=6

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

\(\Leftrightarrow2^n\cdot2^{-1}+2^n\cdot2^2=9\cdot2^5\)

\(\Leftrightarrow2^n\cdot\left(2^{-1}+2^2\right)=9\cdot2^5\)

\(\Leftrightarrow2^n\cdot\dfrac{9}{2}=9\cdot2^5\)

\(\Leftrightarrow2^n=9\cdot2^5:\dfrac{9}{2}=2^5\cdot9\cdot\dfrac{2}{9}=2^6\)

hay n=6

Vậy: n=6

a) \(\frac{1}{9}.27^n=3^n\)

\(=>\frac{27^n}{9}=3^n\)

\(=>3^n=3^n=>n=1\)

b) \(2^{-1}.2^n+4.2^n=9.2^5\)

\(=>2^{n-1}.2^2.2^n=9.2^5\)

\(=>2^{n-1}.2^{2+n}=9.2^5\)

\(=>2^{2n+1}=9.5^2\)

\(=>n=\)

Câu b đề sai hay sao ấy số xấu lắm

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

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

\(2^n.2=288\)

\(2^n=288:2\)

\(2^n=144\)

       Suy ra n ko tìm được

Ta có : 

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

\(=>\left(\frac{1}{2}+4\right)\cdot2^n=9\cdot2^5\)

\(=>\left(\frac{1}{2}+\frac{8}{2}\right)\cdot2^n=9\cdot2^5\)

\(=>\frac{9}{2}\cdot2^n=\frac{9}{2}\cdot2^5\)

\(=>2^n=2^5\)

\(=>n=5\)

2ⁿ.(1/2+4)=9.32

2ⁿ*4,5=288

2ⁿ=64=2⁶

=> n=6

\(2^{-1}.2^n+4.2^n=9.2^5\)

\(2^n.2=9.2^5\)

\(\Rightarrow2^n=9.2^4\)

Ko có n nhé bn

Giúp mk với

a)1/9.27^n=3^n

             3^n=3^n

         =>n={0;1;2;3;...}     

a) n= 2;3;5;7;...(n là số nguyên)

2^-1.2ⁿ + 4.2ⁿ = 9.2⁵

=> 2^n-1 + 2².2ⁿ = 9.2⁵

=> 2^n-1 + 2ⁿ⁺² = 9.2⁵

=> 2^n-1(2³ + 1) = 9.2⁵

=> 2^n-1 . 9 = 9.2⁵

=> 2^n-1 = 2⁵

=> n-1 = 5 => n = 6

2^-1.2ⁿ+4.2ⁿ=9.2⁵

2ⁿ(1/2+4)=288

2ⁿ.9/2=288

2ⁿ=64

2ⁿ=2⁶

n=6

Vậy n=6