Question

Tìm n biết
a) (1/3)^2n-1=243
b) (0,125)^n+1=64

Answer 1

\(\frac{1}{3}^{2n-1}=243\)

\(< =>\frac{1}{3}^{n+n}=\frac{243}{3}=81\)

\(< =>\frac{1}{3^{n+n}}=81\)

\(< =>81.3^n.3^n=1\)

\(< =>3^{2n}=\frac{1}{81}\)

\(< =>3^{2n}=3^{-4}\)

\(< =>x=-2\)

Answer 2

Bài làm:

a) \(\left(\frac{1}{3}\right)^{2n-1}=243\)

\(\Leftrightarrow3^{1-2n}=3^5\)

\(\Rightarrow1-2n=5\)

\(\Leftrightarrow2n=-4\)

\(\Rightarrow n=-2\)

b) \(\left(0,125\right)^{n+1}=64\)

\(\Leftrightarrow\left(\frac{1}{8}\right)^{n+1}=8^2\)

\(\Rightarrow-n-1=2\)

\(\Rightarrow n=-3\)

Answer 3

\(\left(0,125\right)^{n+1}=64\)

\(< =>\left(\frac{1}{8}\right)^{x+1}=\left(\frac{1}{8}\right)^{-2}\)

\(< =>x+1=-2\)

\(< =>x=-2-1=-3\)

Answer 4

a, \(\left(\frac{1}{3}\right)^{2n-1}=243\Leftrightarrow3^{1-2n}=3^5\)

\(\Leftrightarrow1-2n=5\Leftrightarrow2x=-4\Leftrightarrow x=-2\)

b, \(\left(0,125\right)^{n+1}=64\Leftrightarrow3^{1-2n}=3^5\)

\(\Leftrightarrow1-2n=5\Leftrightarrow2n=6\Leftrightarrow n=3\)