Question

[Chibi Yoona]

Tìm n, biết

a. \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)

b. \(\left(\dfrac{7}{5}\right)^n=\dfrac{343}{125}\)

Answer 1

[Trần Minh Hoàng]

a) \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)

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

\(\Rightarrow2n-1=3\)

\(\Rightarrow2n=4\)

\(\Rightarrow n=2\)

Answer 2

[Lưu Hạ Vy]

a) \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)

\(\Rightarrow2^{-\left(2n-1\right)}=2^{-3}\)

\(\Rightarrow2^{-2n+1}=2^{-3}\)

\(\Rightarrow-2n+1=-3\)

\(\Rightarrow-2n=-4\)

\(\Rightarrow n=-2\)

Vậy ...

b) \(\left(\dfrac{7}{5}\right)^n=\dfrac{343}{125}\)

\(\Rightarrow\left(\dfrac{7}{5}\right)^n=\left(\dfrac{7}{5}\right)^3\)

\(\Rightarrow n=3\)

Vậy ....