Question

[bngan ng]

tìm số tự nhiên n biết:

a) 2ⁿ + 2ⁿ⁺⁴ = 272

b) 5ⁿ⁺²- 5ⁿ = 600

Answer 1

[Trịnh Minh Hoàng]

\(a,2^n+2^{n+4}=272\\ \Rightarrow2^n+2^n.2^4=272\\ \Rightarrow2^n+2^n.16=272\\ \Rightarrow2^n.17=272\\ \Rightarrow2^n=16\\ \Rightarrow2^n=2^4\\ \Rightarrow n=4\)

\(b,5^{n+2}-5^n=600\\ \Rightarrow5^n.5^2-5^n=600\\ \Rightarrow5^n\left(25-1\right)=600\\ \Rightarrow5^n.24=600\\ \Rightarrow5^n=25\\ \Rightarrow5^n=5^2\\ \Rightarrow n=2\)

Answer 2

[BÙI LINH ĐAN]

\(a)2^n+2^{n+4}=272\)

\(2^n+2^n.2^4=272\)

\(2^n\left(1+2^4\right)=272\)

\(2^n.17=272\)

\(2^n=16\)

\(2^n=2^4\)

\(\Rightarrow n=4\)

\(b)\)\(5^{n+2}-5^n=600\)

\(5^n.5^2-5^n=600\)

\(5^n\left(5^2-1\right)=600\)

\(5^n.24=600\)

\(5^n=25\)

\(5^n=5^2\)

\(\Rightarrow n=2\)

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