Question

Bài 1: Tính:

a) \(^{27^n}\) : \(^{3^n}\) = 9

b)\(\dfrac{25}{5^n}\)=5

c)\(\dfrac{81}{\left(-3\right)^n}\)=-243

d)\(\dfrac{1}{2}\) . \(^{2^n}\)+\(^{4.2^n}\)=9.25

Giúp mk nha mọi người. Mấy dấu chấm là dấu nhân đó

Answer 1

a,Ta có \(\left(3^3\right)^n:3^n=9\Leftrightarrow3^{3n}:3^n=3^2\Leftrightarrow3n-n=2\Leftrightarrow n=1\)

b,TA có \(\dfrac{5^2}{5^n}=5^1\Leftrightarrow2-n=1\Leftrightarrow n=1\)

Các câu sau để bn tự làm

Answer 2

a) 27ⁿ : 3ⁿ = 9

\(\Leftrightarrow\) (27 : 3)ⁿ = 9

\(\Leftrightarrow\) 9ⁿ = 9

\(\Leftrightarrow\) n = 1

b) \(\dfrac{25}{5^n}=5\)

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

\(\Leftrightarrow5^n.5=5^2\)

\(\Leftrightarrow5^{n+1}=5^2\)

\(\Leftrightarrow n+1=2\)

n = 2 - 1

n = 1

c) \(\dfrac{81}{\left(-3\right)^n}=-243\)

\(\Leftrightarrow\dfrac{\left(-3\right)^4}{\left(-3\right)^n}=\left(-3\right)^5\)

\(\Leftrightarrow\left(-3\right)^n.\left(-3\right)^5=\left(-3\right)^4\)

\(\Leftrightarrow\left(-3\right)^{n+5}=\left(-3\right)^4\)

\(\Leftrightarrow n+5=4\)

n = 4 - 5

n = -1