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a: \(\Leftrightarrow3^n:27^n=\dfrac{1}{9}\)
\(\Leftrightarrow\left(\dfrac{1}{9}\right)^n=\dfrac{1}{9}\)
hay n=1
b: \(\Leftrightarrow3^n\cdot3^2=3^8\)
=>n+2=8
hay n=6
c: \(\Leftrightarrow2^n\cdot\dfrac{9}{2}=9\cdot2^5\)
\(\Leftrightarrow2^n=2^6\)
hay n=6
d: \(\Leftrightarrow8^n=512\)
hay n=3
\(\frac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\)
\(=>\left(\frac{1}{2}+4\right)\cdot2^n=\frac{9}{2}\cdot2^6\)
\(=>\frac{9}{2}\cdot2^n=\frac{9}{2}\cdot2^6\)
\(=>2^n=2^6\)
\(=>n=6\)
\(\frac{1}{32^n}\cdot256^n=2048:2^2\)
\(=>\frac{1}{\left(2^5\right)^n}\cdot\left(2^8\right)^n=2^{10}:2^2\)
\(=>\frac{1}{2^{5n}}\cdot2^{8n}=2^8\)
\(=>2^{3n}=2^8\)
\(=>3n=8\)
\(=>n=\frac{8}{3}\)
\(\frac{1}{9}\). 27n=3n
=> 27n :9 =3n
=> 27n: 3n = 9
(33)n : 3n =9
33n : 3n =9
32n = 9
32n= 32
với 2n = 2
=> n=1
vậy n=1
c, \(\frac{-32}{-2^n}=4\)
\(\Rightarrow-2^n=-32:4\)
\(\Rightarrow-2^n=-8\)
\(\Rightarrow-2^n=-2^3\Rightarrow n=3\)
d, \(\frac{8}{2^n}=2\)
\(\Rightarrow2^n=8:2\)
\(\Rightarrow2^n=4\)
\(\Rightarrow2^n=2^2\Rightarrow n=2\)
e, \(\frac{25^3}{5^n}=25\)
\(\Rightarrow5^n=25^3:25\)
\(\Rightarrow5^n=25^2\)
\(\Rightarrow5^n=5^4\Rightarrow n=4\)
i , \(8^{10}:2^n=4^5\)
\(\Rightarrow2^n=8^{10}:4^5\)
\(\Rightarrow2^n=\left(2^3\right)^{10}:\left(2^2\right)^5\)
\(\Rightarrow2^n=2^{30}:2^{10}\)
\(\Rightarrow2^n=2^{20}\Rightarrow n=20\)
k, \(2^n.81^4=27^{10}\)
\(\Rightarrow2^n=27^{10}:81^4\)
\(\Rightarrow2^n=\left(3^3\right)^{10}:\left(3^4\right)^4\)
\(\Rightarrow2^n=3^{30}:3^{16}\)
\(\Rightarrow2^n=3^{14}\)
\(\Rightarrow2^n=4782969\)Không chia hết cho 2 nên ko có Gt n thỏa mãn
\(\left|x\right|=7\)
\(\Rightarrow\orbr{\begin{cases}x=7\\x=-7\end{cases}}\)
Vậy \(x\in\left\{\pm7\right\}\)
Bạn 12345678901 xuống lớp 1 học đạo đức làm người nhé bạn. Lịch sự tí đi
\(\frac{1}{9}\cdot3^4\cdot3^n=3^8\)
\(=>3^n=3^8:3^4:\frac{1}{9}\)
\(=>3^n=3^8:3^4\cdot9\)
\(=>3^n=3^8:3^4\cdot3^2\)
\(=>3^n=3^6\)
\(=>n=6\)
b) \(\frac{1}{9}.3^4.3^n=3^8\)
\(\Rightarrow\left(\frac{1}{3}\right)^2.3^4.3^n=3^8\)
\(\Rightarrow\frac{1}{3^2}.3^4.3^n=3^8\)
\(\Rightarrow3^2.3^n=3^8\)
\(\Rightarrow3^n=3^8:3^2\)
\(\Rightarrow3^n=3^6\)
\(\Rightarrow n=6\)
Vậy n = 6