Question

Bài 1: Tìm n: A) n⁵¹ = n , B) 1/9 . 27^​n = 3ⁿ​​​

​C) 3^-2 . 3^​4 . 3ⁿ = 3⁷ , D) 32^​-n  . 16ⁿ = 2048

Answer 1

A)n=1, n=1

C) n=5

Answer 2

a) \(n^{51}=n\)

\(\Rightarrow n^{51}-n=0\)

\(n\left(n^{50}-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}n=0\\n^{50}-1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}n=0\\n^{50}=1\end{cases}}\)

\(\Rightarrow n\in\left\{-1;0;1\right\}\)

b) \(\frac{1}{9}.27^n=3^n\)

\(\Rightarrow3^{-2}.3^{3n}=3^n\)

\(3^{3n-2}=3^n\)

\(\Rightarrow3n-2=n\)

\(3n-n=2\)

\(2n=2\)

\(n=2:2=1\)

c) \(3^{-2}.3^4.3^n=3^7\)

\(3^{n+4-2}=3^7\)

\(3^{n+2}=3^7\)

\(\Rightarrow n+2=7\)

\(\Rightarrow n-7=5\)

d) \(32^{-n}.16^n=2048\)

\(2^{-5n}.2^{4n}=2^{10}\)

\(2^{4n-5n}=2^{10}\)

\(2^{-n}=2^{10}\)

\(\Rightarrow-n=10\)

\(\Rightarrow n=-10\)