Question

[Diệp Thiên Giai]

Tìm số nguyên N biết:

\(a,\left(\frac{1}{3}\right)^n=\frac{1}{81}\)

\(b,\frac{-512}{343}=\left(\frac{-8}{7}\right)^n\)

\(c,\left(\frac{-3}{4}\right)^n=\frac{81}{256}\)

\(d,\left(2x+3\right)^2=\frac{9}{121}^n\)

Answer 1

[Nguyễn Huy Tú]

a) \(\left(\frac{1}{3}\right)^n=\frac{1}{81}\)

\(\Rightarrow\left(\frac{1}{3}\right)^n=\frac{1^4}{3^4}\)

\(\Rightarrow\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^4\)

\(\Rightarrow n=4\)

Vậy n = 4

b) \(\frac{-512}{343}=\left(\frac{-8}{7}\right)^n\)

\(\Rightarrow\frac{-8^3}{7^3}=\left(\frac{-8}{7}\right)^n\)

\(\Rightarrow\left(\frac{-8}{7}\right)^3=\left(\frac{-8}{7}\right)^n\)

\(\Rightarrow n=3\)

Vậy n = 3