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a) \(2\cdot16\ge2^n>4\\ 2\cdot2^4\ge2^n>2^2\\ 2^5\ge2^n>2^2\\ \Rightarrow2^n\in\left\{2^3;2^4;2^5\right\}\\ \Rightarrow n\in\left\{3;4;5\right\}\)Vậy \(n\in\left\{3;4;5\right\}\)
b) \(9\cdot27\le3^n\le243\\ 3^2\cdot3^3\le3^n\le3^5\\ 3^5\le3^n\le3^5\\ \Rightarrow3^n=3^5\\ \Rightarrow n=5\)Vậy n = 5
a) \(2.16\ge2^n>4\)
\(\Rightarrow32\ge2^n>4\)
\(\Rightarrow2^5\ge2^n>2^2\)
\(\Rightarrow5\ge n>2\)
\(\Rightarrow\left\{{}\begin{matrix}n=3\\n=4\\n=5\end{matrix}\right.\)
Vậy \(n\in\left\{3;4;5\right\}.\)
b) \(9.27\le3^n\le243\)
\(\Rightarrow243\le3^n\le243\)
\(\Rightarrow3^5\le3^n\le3^5\)
\(\Rightarrow5\le n\le5\)
\(\Rightarrow n=5\)
Vậy \(n=5.\)
Chúc bạn học tốt!
Bài 2:
1: \(5^n+5^{n+2}=650\)
\(\Leftrightarrow5^n\cdot26=650\)
\(\Leftrightarrow5^n=25\)
hay x=2
2: \(32^{-n}\cdot16^n=1024\)
\(\Leftrightarrow\dfrac{1}{32^n}\cdot16^n=1024\)
\(\Leftrightarrow\left(\dfrac{1}{2}\right)^n=1024\)
hay n=-10
13: \(9\cdot27^n=3^5\)
\(\Leftrightarrow3^{3n}=3^5:3^2=3^3\)
=>3n=3
hay n=1
\(\frac{1}{2}.2^n+4.2^n=9.2^5\Rightarrow2^n\left(\frac{1}{2}+4\right)=288\Rightarrow2^n.\frac{9}{2}=288\Rightarrow2^{n-2}.9=288\Rightarrow2^{n-2}=32\)(dấu "=>" số 3 bn sửa thành 2n-1.9=288=>2n-1=32 nha)
=>2n-1=25=>n-1=5=>n=5+1=6
vậy......
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a) \(9.27^n=3^5\Rightarrow3^2.\left(3^3\right)^n=3^5\)
\(\Rightarrow3^2.3^{3n}=3^5\Rightarrow3^{5n}=3^5\)
\(\Rightarrow5n=5\Rightarrow n=1\)
b)\(\left(2^3:4\right).2^n=4\Rightarrow\left(2^3:2^2\right).2^n=2^2\)
\(\Rightarrow2.2^n=2^2\Rightarrow2^{1+n}=2^2\)
\(\Rightarrow1+n=2\Rightarrow n=1\)
c)\(3^2.3^4.3^n=3^7\Rightarrow3^{6+n}=3^7\)
\(\Rightarrow6+n=7\Rightarrow n=1\)
d)\(2^{-1}.2^n+4.2^n=9.2^5\)
\(\Rightarrow2^n\left(2^{-1}+4\right)=3^2.2^5\)
\(\Rightarrow\)\(2^n\left(\frac{1}{2}+4\right)=3^2.2^5\)
\(\Rightarrow\)\(2^n.\frac{3^2}{2}=3^2.2^5\)
\(\Rightarrow\)\(2^{n-1}.3^2=3^2.2^5\)
\(\Rightarrow n-1=5\Rightarrow n=6\)
e)\(243\ge3^n\ge9.3^2\)
\(\Rightarrow3^5\ge3^n\ge3^2.3^2\)
\(\Rightarrow3^5\ge3^n\ge3^4\)
\(\Rightarrow5\ge n\ge4\Rightarrow5;4\)
f)\(2^{n+3}.2^n=128\)
\(\Rightarrow2^{n+3+n}=2^7\)
\(\Rightarrow2^{2n+3}=2^7\)
\(\Rightarrow2n+3=7\Rightarrow2n=4\Rightarrow n=2\)
Hok tối
1, 32 < 2^n < 128
2^5 < 2^n < 2^7
=> 5 < n < 7
Vì n là nguyên dương => n = 6
2, 2.16 > (=) 2^n > 4
2.2^4 > (=) 2^n > 2^2
2^5 > (=) 2^n > 2^2
5 >(=) n > 2 => n = 5 ; 4 ; 3
3, 9.27 < 3^n <= 243
3^2 . 3^3 < 3^n <= 3^5
3^5 < 3^n <=5
5 < n <= 5 ( không có n)
mình làm 1 câu lm mẫu thôi nhé
a) \(2.16\ge2^n>4\)
\(\Rightarrow2.2^4\ge2^n>2^2\)
\(\Rightarrow2^5\ge2^n>2^2\)
\(\Rightarrow5\ge n>2\)
\(\Rightarrow n=5;4;3\)
tíc mình nha
ban giai thich cu the hon dc ko