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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
a) 322n=4
\(\Leftrightarrow\dfrac{2^5}{2^n}=2^2\)
\(\Rightarrow\)\(2^n=2^5:2^2\)
\(\Rightarrow2^n=2^3\)
\(\Rightarrow n=3\)
b) 6255n=5
\(\Leftrightarrow\dfrac{5^4}{5^n}=5^1\)
\(\Rightarrow5^n=5^4:5^1\)
\(\Rightarrow5^n=5^3\)
\(\Rightarrow n=3\)
a) 32 . 3n = 35
=> 3n = 35 : 32
=> 3n = 33
=> n = 3
các câu còn lại tương tự!!
chúc bạn học tốt!! ^^
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a) \(n^{51}=n\)
\(\Rightarrow n^{51}-n=0\)
\(n\left(n^{50}-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}n=0\\n^{50}-1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}n=0\\n^{50}=1\end{cases}}\)
\(\Rightarrow n\in\left\{-1;0;1\right\}\)
b) \(\frac{1}{9}.27^n=3^n\)
\(\Rightarrow3^{-2}.3^{3n}=3^n\)
\(3^{3n-2}=3^n\)
\(\Rightarrow3n-2=n\)
\(3n-n=2\)
\(2n=2\)
\(n=2:2=1\)
c) \(3^{-2}.3^4.3^n=3^7\)
\(3^{n+4-2}=3^7\)
\(3^{n+2}=3^7\)
\(\Rightarrow n+2=7\)
\(\Rightarrow n-7=5\)
d) \(32^{-n}.16^n=2048\)
\(2^{-5n}.2^{4n}=2^{10}\)
\(2^{4n-5n}=2^{10}\)
\(2^{-n}=2^{10}\)
\(\Rightarrow-n=10\)
\(\Rightarrow n=-10\)
a) Ta có: \(\frac{1}{9}\cdot27^n=3^n\)
\(\Leftrightarrow\frac{1}{3^2}\cdot\left(3^3\right)^n=3^n\)
\(\Leftrightarrow3^{3n}=3^{n+2}\)
\(\Rightarrow3n=n+2\)
\(\Rightarrow n=1\)
b) Ta có: \(3^2.3^4.3^n=3^7\)
\(\Rightarrow3^n=3\)
\(\Rightarrow n=1\)
c) Ta có: \(2^{-1}.2^n+4.2^n=9.2^5\)
\(\Leftrightarrow2^n\cdot\frac{9}{2}=9.2^5\)
\(\Rightarrow2^n=2^6\)
\(\Rightarrow n=6\)
d) Ta có: \(32^{-n}.16^n=2048\)
\(\Leftrightarrow\frac{1}{2^{5n}}\cdot2^{4n}=2^{11}\)
\(\Leftrightarrow2^{4n}=2^{5n+11}\)
\(\Rightarrow4n=5n+11\)
\(\Rightarrow n=-11\)
a,
\(\dfrac{2^n}{32}=4\\ 2^n:2^5=2^2\\ 2^n=2^2\cdot2^5\\ 2^n=2^7\\ n=7\)
b,
\(27^n\cdot9^n=9^{27}:81\\ \left(3^3\right)^n\cdot\left(3^2\right)^n=\left(3^2\right)^{27}:3^4\\ 3^{3n}\cdot3^{2n}=3^{54}:3^4\\ 3^{3n+2n}=3^{50}\\ 3^{5n}=3^{50}\\5n=50\\ n=10 \)
a. n = 7
b. n = 10