Tìm số tự nhiên n biết:
\(\frac{1}{9}.27^n=3^n\)
\(3^{-2}.3^4.3^n=3^7\)
\(2^{-1}.2^n+4.2^n=9.2^5\)
\(32^{-n}.16^n=2048\)
Tìm x thuộc Z biết:
\(2^{x+2}-2^x=96\)
\(7^{x+2}+2.7^{x-1}=345\)
\(3^{x-1}+5.3^{x-1}=162\)
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 tự nhiên n biết:
\(\frac{1}{9}.27^n=3^n\)
\(3^{-2}.3^4.3^n=3^7\)
\(2^{-1}.2^n+4.2^n=9.2^5\)
\(32^{-n}.16^n=2048\)
Tìm x thuộc Z biết:
a) 2x+2-2x=96 b) 7x+2+2.7x-1=345 c) 3x-1+5.3x-1=162
Thu gọn tổng sau:
A=1+3+32+33+...+3100 B= 2100-299-298-297-...-22-2 C= 3100-399+398-397-...+32-3+1
2) a) 2x.(22 - 1) = 96 => 2x. 3 = 96 => 2x = 96 : 3 = 32 = 25 => x = 5
b) 7x. (72 + 2. 7-1) = 345 => 7x. \(\frac{345}{7}\) = 345 => 7x = 7 => x = 1
c) 3x-1. (1 + 5) = 162 => 3x-1 . 6 = 162 => 3x-1 = 162 : 6 = 27 = 33 => x - 1 = 3 => x = 3 + 1 = 4
1) a) (33)n = 9.3n => 33n = 32.3n = 32+n => 3n = 2 + n => 3n - n = 2 => 2n = 2 => n = 1
b) 3-2+4+n = 37 => 2 + n = 7 => n = 7 - 2 = 5
c) 2n.(2-1 + 4) = 9.25 => 2n.\(\frac{9}{2}\) = 9.25 => 2n-1 = 25 => n - 1 = 5 => n = 5 + 1 = 6
d) (25)-n.(24)n = 211 => 2-5n. 24n = 211 => 2-5n+4n = 211 => 2-n = 211 => -n = 11 => n = -11
3) 3.A = 3 + 32 + 33 + ...+ 3101
=> 3.A - A = 3101 - 1 => 2.A = 3101 - 1 => A = (3101 - 1)/ 2
b) 2. B = 2101 - 2100 - 299 - ...- 23 - 22 => 2.B - B = 2101 - 2.2100 + 2 = 2 => B = 2
c) 3. C = 3101 - 3100 + 399 - 398 -....+ 33 - 32 + 3
=> 3. C - C = 3101 + 1 => 2C = 3301 + 1 => C = (3301 + 1) / 2
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 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 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) \(32^{-n}.16^n=2048\)
Bạn tham khảo tại đây nhé: Câu hỏi của Khánh Huyền⁀ᶦᵈᵒᶫ .
Chúc bạn học tốt!
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)
Bài 1 Tính
a,(1/3)^-1 - (-6/7)^0 +(1/2)^2:2
b,[(0,1)^2]^0+[1/7^-1]^2 x 1/49 x [(2^2)^3:2^5]
Bài 2 Tìm số nguyên n biết
a,1/9 x 27^n=3^n
b,3^-2 x 3^4 x 3^n =3^7
c,2^-1 x 2^n 4 x 2^-n=9 x 2^5
d,32^-n x 16^n=2048
e, (n-2)^1=16
f, (2n+1)^3=-27
giải chi tiết hộ mk nhé
giải luôn hộ mk hnay mk phải đi học r
Tìm x thuộc Z
a)\(32^{-n}.16^n=2048\)
b)\(2^{-1}.2^n+4.2^n=9.2^5\)
a)\(32^{-n}\cdot16^n=2048\)
\(\left(2^5\right)^{-n}\cdot\left(2^4\right)^n\)=2048
\(2^{-5n}\cdot2^{4n}\)=\(2^{11}\)
\(2^{-5n+4n}=2^{11}\)
\(2^{-x}=2^{11}\)
\(\Rightarrow x=-11\)
b)\(2^{-1}\cdot2^n+4\cdot2^n=9\cdot2^5\)
\(\frac{1}{2}\cdot2^n+4\cdot2^n=288\)
\(2^n\left(\frac{1}{2}+4\right)=288\)
\(2^n\cdot\frac{9}{2}=288\)
\(2^n=288:\frac{9}{2}\)
\(2^n=64\)
\(2^n=2^6\)
\(\Rightarrow n=6\)
a) 32-n . 16n = 2048
\(\frac{1}{32n}\) . 16n = 2048
\(\frac{1}{2^n.16^n}\) . 16n = 2048
\(\frac{1}{2^n}\) = 2048
2-n = 2048
2-n = 211
\(\Rightarrow\) -n = 11
\(\Rightarrow\) n = -11
Vậy n = -11
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) \(3^{-1}.3^n+4.3^n=13.3^7\)
\(32^{-n}.16^n=2048\)
HELP ME NOW