Question

Tìm số nguyên n, biết: 2^-1.2ⁿ+ 4.2ⁿ =9.2⁵

Answer 1

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

Answer 2

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

Answer 3

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

=> \(2^n(2^{-1}+4)=9.2^5\)

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

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

=> \(2^{n-1}.9=9.2^5\)

=> \(\dfrac{9}{9}=\dfrac{2^{n-1}}{2^5}\)
=> \(1=\dfrac{2^{n-1}}{2^5}\)

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

=> \(\left\{{}\begin{matrix}n-1=5\\\Rightarrow n=6\end{matrix}\right.\)

Answer 4

Cảm ơn nhiều lắm!!!