Question

[thần nông đáng iu]

TÌM SỐ NGUYÊN n SAO CHO:

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

Answer 1

[Minh Hiền]

\(\frac{2^n}{2}+2^2.2^n=9.2^5\)

=> \(2^{n-1}+2^{2+n}=2^5.9\)

=> \(2^{n-1}+2^{n-1+3}=2^5.9\)

=> \(2^{n-1}.\left(1+2^3\right)=2^5.9\)

=> \(2^{n-1}.9=2^5.9\)

=> \(2^{n-1}=2^5\)

=> \(n-1=5\)

Vậy n = 6.

Answer 2

[Hotaru Takegawa]

Ta có:

\(\frac{2^n}{2}+2^2.2^n=2^{n-1}+2^3.2^{n-1}=2^{n-1}.\left(1+2^3\right)\)

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

Chia cả 2 vế cho 9 thì có:

\(2^{n-1}=2^5\Rightarrow2^n=2^6\Rightarrow n=6\)