Question

a) \(\dfrac{32}{2^n}=4\)

b) \(\dfrac{625}{5^n}=5\)

c) \(27^n:3^n=3^2\)

Answer 1

a)\(\dfrac{32}{2^n}=4\)

\(\Rightarrow2^n=32:4\)

\(\Leftrightarrow2^n=8\) =2³

\(\Rightarrow n=3\)

b)\(\dfrac{625}{5^n}=5\)

\(\Rightarrow5^n=625:5\)

\(\Leftrightarrow5^n=125\)=5³

^{\(\Rightarrow n=3\)}

c)27ⁿ:3ⁿ=3²

^{\(\Leftrightarrow\left(3^3\right)^n:3^n=3^2\)}

\(\Leftrightarrow3^{3n}:3^n=3^2\)

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

\(\Rightarrow3^{2n}=3^2\)

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

CHÚC BẠN HỌC TỐT

Answer 2

a) $\frac{32}{2^n}=4$

\(\Leftrightarrow\dfrac{2^5}{2^n}=2^2\)

\(\Rightarrow\)\(2^n=2^5:2^2\)

\(\Rightarrow2^n=2^3\)

\(\Rightarrow n=3\)

b) $\frac{625}{5^n}=5$

\(\Leftrightarrow\dfrac{5^4}{5^n}=5^1\)

\(\Rightarrow5^n=5^4:5^1\)

\(\Rightarrow5^n=5^3\)

\(\Rightarrow n=3\)

Answer 3

a. \(\dfrac{32}{2^n}=4\)

\(\Rightarrow2^n.4=32\)

\(\Rightarrow2^n=32:4=8\)

\(\Rightarrow2^n=2^3\)

\(\Rightarrow n=3\)

Vậy...

b. \(\dfrac{625}{5^n}=5\)

\(\Rightarrow5^n.5=625\)

\(\Rightarrow5^n=625:5=125\)

\(\Rightarrow5^n=5^3\)

\(\Rightarrow n=3\)

Vậy...

c. \(27^n:3^n=3^2\)

\(\Rightarrow\left(3^3\right)^n:3^n=3^2\)

\(\Rightarrow3^{3n}:3^n=3^2\)

\(\Rightarrow3n+n=2\)

\(\Rightarrow4n=2\)

\(\Rightarrow n=2:4=\dfrac{1}{2}\)

Vậy...

Answer 4

a) \(\dfrac{32}{2^n}\) = 4

32 : 2ⁿ = 4

2ⁿ = 32 : 4

2ⁿ = 8

\(\Rightarrow\) 2ⁿ = 2³

\(\Rightarrow\) n = 3.

b) \(\dfrac{625}{5^n}\) = 5

625 : 5ⁿ = 5

5ⁿ = 625 : 5

5ⁿ = 125

\(\Rightarrow\) 5ⁿ = 5³

\(\Rightarrow\) n = 3.

c) 27ⁿ : 3ⁿ = 3²

27ⁿ : 3ⁿ = 9

- Nếu n = 1 thì 27¹ : 3¹ = 9 (chọn).

- Nếu n \(\ge\) 2 thì 27ⁿ : 3ⁿ = 9 (vô lý)

Vậy n = 1.

Answer 5

Giải:

a) \(\dfrac{32}{2^n}=4\)

\(\Leftrightarrow2^n=\dfrac{32}{4}\)

\(\Leftrightarrow2^n=8\)

\(\Leftrightarrow2^n=2^3\)

Vì \(2=2\)

Nên \(n=3\).

b) \(\dfrac{625}{5^n}=5\)

\(\Leftrightarrow5^n=\dfrac{625}{5}\)

\(\Leftrightarrow5^n=125\)

\(\Leftrightarrow5^n=5^3\)

Vì \(5=5\)

Nên \(n=3\).

c) \(\dfrac{27^n}{3^n}=3^2\)

\(\Leftrightarrow\dfrac{\left(3^3\right)^n}{3^n}=3^2\)

\(\Leftrightarrow\dfrac{3^{3n}}{3^n}=3^2\)

\(\Leftrightarrow3^{3n}=3^n.3^2\)

\(\Leftrightarrow3^{3n}=3^{n+2}\)

Vì \(3=3\)

Nên \(3n=n+2\)

\(\Leftrightarrow3n-n=2\)

\(\Leftrightarrow2n=2\)

\(\Leftrightarrow n=1\).

Chúc bạn học tốt!

Answer 6

ôi trời, con c mỗi ng 1 đáp số, nhìn ai cx thấy có ý đúng