Question

tìm số tự nhiên n biết : 

2 ⁿ + 2 ^{n + 3}  = 144

Answer 1

2ⁿ+2ⁿ⁺³=144

=>2ⁿ+2ⁿ⁺³=2⁴+2⁷

=>n+n+3=4+7

=>2n+3=11

2n=8

n=4

Answer 2

2ⁿ+2ⁿ⁺³=2ⁿ+2ⁿ.2³=2ⁿ(1+8)=2ⁿ.9=144

=>2ⁿ=144:9=16

=>2ⁿ=2⁴

=>n=4

vậy...

Answer 3

\(2^n+2^{n+3}=144.\)

\(2^n.1+2^n.2^3=144.\)

\(2^n\left(1+2^3\right)=144.\)

\(2^n\left(1+8\right)=144.\)

\(2^n.9=144.\)

\(2^n=144:9.\)

\(2^n=16.\)

\(2^n=2^4\Rightarrow n=4\in N.\)

Vậy \(n=4.\)