Question

Tìm n

(1/3)².27ⁿ=3ⁿ

Answer 1

\(\left(\frac{1}{3}\right)^2\cdot27^n=3^n\)

\(\left(\frac{1}{3}\right)^2=3^n^{-3n}\)

\(\left(\frac{1}{3}\right)^2=3^{-2n}\)

\(\left(\frac{1}{3}\right)^2=\left(3^{-n}\right)^2\)

\(\frac{1}{3}=3^{-n}\)

\(n=1\)

Answer 2

\(\left(\frac{1}{3}\right)^2.27^n=3^n\)

\(\Leftrightarrow\left(\frac{1}{3}\right)^2=\left(\frac{3}{27}\right)^n\)

\(\Leftrightarrow\frac{1}{9}=\left(\frac{1}{9}\right)^n\)

\(\Leftrightarrow n=1\)