Question

Tìm các số tự nhiên biết: 

a) \(2^{n-1}:2=256\)

b) \(5^n+5^{n-2}=650\)

c) \(2^{n-3}+2^{n+1}=136\)

Answer 1

2^n-1:2=256

2^n-1=512=2⁹=>n-1=9=>n=10

5ⁿ+5^n-2=650

5^n-2(25+1)=650=>5^n-2=25=5²

=>n-2=2=>n=4

Answer 2

a) \(2^{n-1}:2=256\)

\(2^{n-1-1}=256\)

\(2^{n-2}=2^8\)

\(\Rightarrow n-2=8\)

\(\Rightarrow n=10\)

vay \(n=10\)

Answer 3

2^n-3+2ⁿ⁺¹=136

2^n-3(16+1)

=2^n-3x17=136=>2^n-3=8=2³

=>n-3=3=>n=6

Answer 4

a) \(2^{n-1}:2=256\)

\(2^{n-2}=256\)

\(2^{n-2}=2^8\)

\(\Rightarrow n-2=8\)

\(\Rightarrow n=10\)

vậy \(n=10\)