Question

Tìm số tự nhiên n, biết :

a) \(\dfrac{16}{2^n}\)=2

b) \(\dfrac{\left(-3\right)^n}{81}\)=-27

c) 8ⁿ:2ⁿ=4

Answer 1

a, \(\dfrac{16}{2^n}=2\)

\(2^n=\dfrac{16}{2}\)

\(2^n=8\)

\(2^n=2^3\)

=> n = 3

b, \(\dfrac{\left(-3\right)^n}{81}=-27\)

\(\left(-3\right)^n=-27\cdot81\)

\(\left(-3\right)^n=\left(-3\right)^3\cdot3^4\)

\(\left(-3\right)^n=\left(-3\right)^7\)

=> n = 7

c, \(8^n:2^n=4\)

\(2^{3n}:2^n=2^2\)

\(2^{2n}=2^2\)

=> 2n = 2

n = 2:2

n = 1

Answer 2

a )

\(\dfrac{16}{2^n}=2\) \(\Leftrightarrow16:x=2\)

\(\Rightarrow x=8\)

\(2^n=8\Rightarrow n=3\)

b )

\(\dfrac{\left(-3\right)^n}{81}=-27\) \(\Leftrightarrow x=-27.81\)

\(\Rightarrow x=-2187\)

\(\left(-3\right)^n=-2187\Rightarrow n=7\)

c )

\(8^n:2^n=4\Leftrightarrow4^n=4\)

\(\Rightarrow n=1\)

Answer 3

(2^2:4)*2^n=4

3^2*3^4*3^n=3^7