Question

Tìm số tự nhiên n , biết :

a ) \(\frac{64}{2^n}=16\)

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

Answer 1

a, \(\frac{64}{2^n}=16\Leftrightarrow\frac{64}{2^n}=\frac{64}{4}\Leftrightarrow2^n=4\Leftrightarrow n=2\)

b, \(\left(\frac{1}{3}\right)^{2n-1}=\left(\frac{1}{3}\right)^3\Leftrightarrow2n-1=3\Leftrightarrow n=2\)

Answer 2

a)\(\frac{64}{2^n}=16\Leftrightarrow2^n.16=64\Leftrightarrow2^n=4\Leftrightarrow2^n=2^2\Leftrightarrow n=2\)

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

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

\(\Leftrightarrow2n-1=3\Leftrightarrow2n=4\Leftrightarrow n=2\)

Answer 3

a) \(\frac{64}{2^n}=16\Leftrightarrow64=16.2^n\Leftrightarrow2^n=4\Leftrightarrow2^n=2^2\Leftrightarrow n=2\)

Vậy: \(n=2\)

b) \(\left(\frac{1}{3}\right)^{2n-1}=\frac{1}{27}\Leftrightarrow\left(\frac{1}{3}\right)^{2n-1}=\left(\frac{1}{3}\right)^3\Leftrightarrow2n-1=3\Leftrightarrow2n=4\Leftrightarrow n=2\)

Vậy: \(n=2\)

Answer 4

\(\frac{64}{2^n}=16=>\frac{4}{2^n}=>\frac{2^2}{2^n}=>n=2\)

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

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

2n-1=3

2n=3+1

2n=4

n=4:2

n=2

vậy n=2