Question

Tìm số tự nhiên n, biết

a)

b)

c)

Answer 1

a) \(\dfrac{16}{2^n}=2\Rightarrow2^n=\dfrac{16}{2}=8=2^3\)

\(\Rightarrow n=3\)

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

\(\Leftrightarrow\dfrac{\left(-3\right)^n}{3^4}=\left(-3\right)^3\)

\(\Leftrightarrow\left(-3\right)^n=-\left(3^4\cdot3^3\right)=\left(-3\right)^7\)

\(\Rightarrow n=7\)

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

\(\Leftrightarrow2^{3n}:2^n=2^2\)

\(\Leftrightarrow3n-n=2\)

\(\Leftrightarrow2n=2\Rightarrow n=1\)

Answer 2

a, \(\dfrac{16}{2^n}=2\Rightarrow2^n.2=16\Rightarrow2^{n+1}=2^4\Rightarrow n+1=4\Rightarrow n=3\). Vậy n=3.

b, \(\dfrac{\left(-3\right)^n}{81}=-27\Rightarrow\left(-3\right)^n=81.\left(-27\right)\Rightarrow\left(-3\right)^n=-2187\)

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

Vậy n=7

c, \(8^n:2^n=4\Rightarrow\left(2^3\right)^n:2^n=2^2\Rightarrow2^{3n}:2^n=2^2\Rightarrow2^{2n}=2^2\Rightarrow2n=2\Rightarrow n=1\)

Vậy n=1.

Answer 3

a)

\(\dfrac{16}{2^n}=2\\ =>2.2^n=16\\ < =>2^n=\dfrac{16}{2}=8\\ Mà:2^3=8\\ =>2^3=2^n\\ =>n=3\)

b) \(\dfrac{\left(-3\right)^n}{81}=-27\\ < =>-27.81=\left(-3\right)^n\\ < =>\left(-3\right)^3.\left(-3\right)^4=\left(-3\right)^n\\ < =>\left(-3\right)^7=\left(-3\right)^n\\ =>n=7\)

c) \(8^n:2^n=4\\ < =>\left(8:2\right)^n=4\\ < =>4^n=4\\ Mà:4^1=4\\ =>4^n=4^1\\ =>n=1\)

Answer 4

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

\(\Leftrightarrow\) 16 : \(2^n\) = 2

\(\Leftrightarrow\) \(2^n\) = 16 : 2

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

\(\Rightarrow\) \(n\) = 3

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

\(\Leftrightarrow\) \(\left(-3\right)^n\) : 81 = \(-27\)

\(\Leftrightarrow\) \(\left(-3\right)^n\) = \(-27\) . 81

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

\(\)\(\Rightarrow\) \(n\) = 7

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

\(\Leftrightarrow\) \(4^{n^2}\) = 4

\(\Rightarrow\) n = 1

Answer 5

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

\(\Rightarrow2.2^n=16\)

\(\Rightarrow4^n=4^2\)

=> n = 2

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

\(\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^4}=\left(-3\right)^3\)

\(\Rightarrow\left(-3\right)^n=\left(-3\right)^3.\left(-3\right)^4\)

\(\Rightarrow\left(-3\right)^n=\left(-3\right)^{3+4}\)

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

=> n = 7

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

\(\Rightarrow\left(8:2\right)^n=4\)

\(\Rightarrow4^n=4\)

=> n = 1