Bài 32 : Tìm số nguyên n , biết :
a) \(\frac{1}{9}.27^n=3^n\)
b) \(3^{-2}.3^4.3^n=3^7\)
c) \(2^{n-1}.2^n+4.2^n=9.2^5\)
d) \(32^{-n}.16^n=2048\)
Bài 32 : Tìm số nguyên n , biết :
a) \(\frac{1}{9}.27^n=3^n\)
b) \(3^{-2}.3^4.3^n=3^7\)
c) \(2^{-1}.2^n+4.2^n=9.2^5\)
d) \(32^{-n}.16^n=2048\)
a) \(\frac{1}{9}.27^n=3^n\)
\(\Leftrightarrow3^{-2}.3^{3n}=3^n\)
\(\Leftrightarrow3^{3n-2}=3^n\)
\(\Leftrightarrow3n-2=n\)
\(\Leftrightarrow2n=2\)
\(\Leftrightarrow n=1\)
b)\(3^{-2}.3^4.3^n=3^7\)
\(\Leftrightarrow3^{2+n}=3^7\)
\(\Leftrightarrow2+n=7\)
\(\Leftrightarrow n=5\)
c) \(2^{-1}.2^n+4.2^n=9.2^5\)
\(\Leftrightarrow2^n\left(4+\frac{1}{2}\right)=9.2^5\)
\(\Leftrightarrow2^n.\frac{9}{2}=9.2^5\)
\(\Leftrightarrow2^{n-1}=2^5\)
\(\Leftrightarrow n-1=5\Leftrightarrow n=6\)
Tìm số nguyên n biết: 1/9.27^n=3^n. b)3^-2.3^4.3^n=3^7. c) 2^n-1.2^n+4.2^n=9.2^5. d)32^-n.16^n=2048. Các bạn giải hộ mình nhé
a)1/9.27^n=3^n
3^n=3^n
=>n={0;1;2;3;...}
a) n= 2;3;5;7;...(n là số nguyên)
Tìm n thuộc Z biết:
a)\(\frac{1}{9}.27^n=3^n\)
b) \(3^2.3^4.3^n=3^7\)
c) \(2^{-1}.2^n+4.2^n=9.2^5\)
d) \(32^{-n}.16^n=2048\)
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: \(32^{-n}.16^n=2048\)
\(\Leftrightarrow\frac{1}{2^{5n}}\cdot2^{4n}=2^{11}\)
\(\Leftrightarrow2^{4n}=2^{5n+11}\)
\(\Rightarrow4n=5n+11\)
\(\Rightarrow n=-11\)
Tìm số nguyên n biết: 1/9.27^n=3^n. b)3^-2.3^4.3^n=3^7. c) 2^n-1.2^n+4.2^n=9.2^5. d)32^-n.16^n=2048. Các bạn giải hộ mình nhé
Toán lớp 6
a)1/9.27^n=3^n
3^n=3^n
=>n={0;1;2;3...}
Tích nha ^_^ !!!
Tìm \(n\in Z\)
a/\(\dfrac{1}{9}.27^n=3^n\)
b/\(3^{-2}.3^4.3^n=3^7\)
c/\(2^{-1}.2n+4.2^n=9.2^5\)
d/\(32^{-n}.16^n=2048\)
a)\(\dfrac{1}{9}.27^n=3^n\)
<=>27n=3n:\(\dfrac{1}{9}\)
<=>27n:3n=\(\dfrac{1}{9}\)
<=>33n:3n=\(\dfrac{1}{9}\)
<=>32n=\(\dfrac{1}{9}\)
<=>9n=\(\dfrac{1}{9}\)
<=>9n+1=1
<=>n+1=0
<=>n=-1
vậy n=-1
Tìm x:
a) \(\frac{1}{9}.27^n=3^n\)
b) \(3^{-2}.3^4.3^n=3^7\)
c) \(2^{-1}.2^n+4.2^n=9.2^5\)
d) \(32^{-n}.16^n=2048\)
a, \(\frac{1}{9}.27^n=3^n\Leftrightarrow\frac{1}{9}.3^{3.n}=3^n\Leftrightarrow\frac{1}{3^2}=3^n:3^{3n}\Leftrightarrow\frac{1}{3^2}=3^{n-3n}=3^{2n}\)
=> 3^2n . 3^2 = 1 => 3^( 2n + 2) = 3^0 => 2n + 2 = 0 => 2n = - 2 => n = - 1
b, 3^-2.3^4 .3^n = 3^ 7 => 3^ ( -2 + 4 + n) = 3^7 => 3^ (n+ 2) = 3^7 => n + 2 = 7 => n = 5
Bài 1: tìm n\(\in N\)
a) \(\frac{1}{9}.27^n=3^n\)
b) \(\frac{1}{9}.3^4.3^n=3^8\)
c)\(\frac{1}{2}.2^n+4.2^n=9.2^5\)
d) \(\frac{1}{32^n}.256^n=2048:2^2\)
giải nhanh giúp với mai mk nộp rồi minh hứa sẽ đền ơn xứng đáng mà cảm ơn
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
Bài 5: tìm \(n\in N\)
a) \(\frac{1}{9}\). 2n = 3n
b) \(\frac{1}{9}.3^4.3^n=3^8\)
c) \(\frac{1}{2}.2^n+4.2^n=9.2^5\)
d) \(\frac{1}{32^n}.256^n=2048:2^2\)
giải hết giúp với mai mình nộp rồi cảm ơn mk sẽ bảo mấy đứa bạn mk tick cho nhé
bài 1 : tìm GTLN : M = 3 - /5-x/
N = 10 - /x+2/ - /1-y/
Bài 2: tìm n
a ) 32< 2n < 128
b)\(\frac{1}{9}.27^n=3^n\)
c) \(3^{-1}.3^n+4.3^n=13.3^7\)
\(32^{-n}.16^n=2048\)
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