bài 1 Tìm n thuộc Z
a, \(27^n:3^n=9\) b,\(\frac{811}{\left(-3\right)^n}=-243\) \(c,\left(\frac{-3}{4}\right)^n=\frac{81}{256}\)
Những câu hỏi liên quan
tìm số nguyên x
a)\(27^n:3^n=9\)
b)\(\left(\frac{-1}{3}\right)^N=\frac{1}{81}\)c)\(\frac{25}{5^n}=5\)d)\(\frac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\)e)\(\frac{81}{\left(-3\right)^n}=-243\)
Bn nào giải đc câu nào thì giải nhé ko giải đc câu nào thì thôi
a)Tìm số nguyên dương n thỏa mãn:
\(\frac{1}{2}.\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{n.\left(n+2\right)}\right)=\frac{2013}{2014}\)
b)tìm a sao cho
\(\left(a+\frac{1}{1.3}\right)+\left(a+\frac{1}{3.5}\right)+\left(a+\frac{1}{5.7}\right)+...+\left(a+\frac{1}{23.25}\right)=11.a+\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\right)\)
Tìm n∈Z biết :
a,27n/3n
b,frac{25}{5^n}5
c,frac{81}{left(-3right)^n}-243
d,frac{1}{2}cdot2^n+4cdot2^n9cdot2^5
e,(frac{1}{3})nfrac{1}{81}
f,left(frac{-3}{4}right)^nfrac{81}{256}
g,frac{-512}{343}left(frac{-8}{7}right)^n
h,5-1*25n125
k,3-1*3n+6*3n-17*36
Đọc tiếp
Tìm n∈Z biết :
a,27n/3n
b,\(\frac{25}{5^n}\)=5
c,\(\frac{81}{\left(-3\right)^n}=-243\)
d,\(\frac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\)
e,(\(\frac{1}{3}\))n=\(\frac{1}{81}\)
f,\(\left(\frac{-3}{4}\right)^n=\frac{81}{256}\)
g,\(\frac{-512}{343}=\left(\frac{-8}{7}\right)^n\)
h,5-1*25n=125
k,3-1*3n+6*3n-1=7*36
a) Câu này thiếu đề nhé bạn.
b) \(\frac{25}{5^n}=5\)
\(\Rightarrow5^n=25:5\)
\(\Rightarrow5^n=5\)
\(\Rightarrow5^n=5^1\)
\(\Rightarrow n=1\)
Vậy \(n=1.\)
c) \(\frac{81}{\left(-3\right)^n}=-243\)
\(\Rightarrow\left(-3\right)^n=81:\left(-243\right)\)
\(\Rightarrow\left(-3\right)^n=-\frac{1}{3}\)
\(\Rightarrow\left(-3\right)^n=\left(-3\right)^{-1}\)
\(\Rightarrow n=-1\)
Vậy \(n=-1.\)
e) \(\left(\frac{1}{3}\right)^n=\frac{1}{81}\)
\(\Rightarrow\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^4\)
\(\Rightarrow n=4\)
Vậy \(n=4.\)
f) \(\left(-\frac{3}{4}\right)^n=\frac{81}{256}\)
\(\Rightarrow\left(-\frac{3}{4}\right)^n=\left(-\frac{3}{4}\right)^4\)
\(\Rightarrow n=4\)
Vậy \(n=4.\)
Chúc bạn học tốt!
d) \(\frac{1}{2}.2^n+4.2^n=9.2^5\)
\(\Rightarrow2^n.\left(\frac{1}{2}+4\right)=288\)
\(\Rightarrow2^n.\frac{9}{2}=288\)
\(\Rightarrow2^n=288:\frac{9}{2}\)
\(\Rightarrow2^n=64\)
\(\Rightarrow2^n=2^6\)
\(\Rightarrow n=6\)
Vậy \(n=6.\)
g) \(-\frac{512}{343}=\left(-\frac{8}{7}\right)^n\)
\(\Rightarrow\left(-\frac{8}{7}\right)^n=\left(-\frac{8}{7}\right)^3\)
\(\Rightarrow n=3\)
Vậy \(n=3.\)
h) \(5^{-1}.25^n=125\)
\(\Rightarrow5^{-1}.5^{2n}=5^3\)
\(\Rightarrow5^{-1+2n}=5^3\)
\(\Rightarrow-1+2n=3\)
\(\Rightarrow2n=3+1\)
\(\Rightarrow2n=4\)
\(\Rightarrow n=4:2\)
\(\Rightarrow n=2\)
Vậy \(n=2.\)
k) \(3^{-1}.3^n+6.3^{n-1}=7.3^6\)
\(\Rightarrow3^{n-1}+6.3^{n-1}=7.3^6\)
\(\Rightarrow3^{n-1}.\left(1+6\right)=7.3^6\)
\(\Rightarrow3^{n-1}.7=7.3^6\)
\(\Rightarrow n-1=6\)
\(\Rightarrow n=6+1\)
\(\Rightarrow n=7\)
Vậy \(n=7.\)
Chúc bạn học tốt!
b)\(\frac{25}{5^n}\)=5
\(5^n\)=25/5
\(5^n\)=\(5^1\)
⇒ n = 1
c) \(\frac{81}{\left(-3\right)^n}\)=-243
\(\left(-3\right)^n\)=81/-243
\(\left(-3\right)^n\)=\(\frac{-1}{3}\)
\(\left(-3\right)^n\)=\(\left(-3\right)^{-1}\)
⇒n=-1
bài1: tìm x:a)8 2^x 2^9.2^5b)27 81^3:3^x 243c)left(frac{2}{5}right)^xleft(frac{5}{2}right)^{-3}.left(frac{-2}{5}right)^2d)left(5x+1right)^2frac{36}{49}e)left(x-frac{2}{9}right)^3left(frac{2}{3}right)^6 f)left(8x-1right)^{2n+1}5^{2n+1}(n thuộc N)bài 2:tìm x,y biết:a)x^2+left(y-frac{1}{10}right)^40b)left(frac{1}{2}x-5right)^{20}+left(y^2-frac{1}{4}right)^{10} 6c)left(x-7right)^{x+1}-left(x-yright)^{x+11}0bài 3:tìm giá trị nhỏ nhất:Aleft(2x+frac{1}{3}right)^2-1tìm Gía...
Đọc tiếp
bài1: tìm x:
a)\(8< 2^x< =2^9.2^5\)
b)\(27< 81^3:3^x< 243\)
c)\(\left(\frac{2}{5}\right)^x\left(\frac{5}{2}\right)^{-3}.\left(\frac{-2}{5}\right)^2\)
d)\(\left(5x+1\right)^2=\frac{36}{49}\)
e)\(\left(x-\frac{2}{9}\right)^3=\left(\frac{2}{3}\right)^6\) f)\(\left(8x-1\right)^{2n+1}=5^{2n+1}\)(n thuộc N)
bài 2:tìm x,y biết:
a)\(x^2+\left(y-\frac{1}{10}\right)^4=0\)
b)\(\left(\frac{1}{2}x-5\right)^{20}+\left(y^2-\frac{1}{4}\right)^{10}< =6\)
c)\(\left(x-7\right)^{x+1}-\left(x-y\right)^{x+11}=0\)
bài 3:tìm giá trị nhỏ nhất:
\(A=\left(2x+\frac{1}{3}\right)^2-1\)
tìm Gía trị lớn nhất :\(B=-\left(\frac{4}{9}x-\frac{2}{15}\right)^6+3\)
baif4: tìm x,y:
\(x.\left(x-y\right)=\frac{1}{10}\) \(\)
giúp mình với nhé
1.
a) \(x\in\left\{4;5;6;7;8;9;10;11;12;13\right\}\)
b) x=0
d) \(x=\frac{-1}{35}\) hoặc \(x=\frac{-13}{35}\)
e) \(x=\frac{2}{3}\)
Tìm số nguyên n, biết rằng:
a) \(27^n:3^n=9\)
b) \(\left(\frac{25}{5}\right)^n=5\)
c)\(\frac{81}{\left(-3\right)^n}=-243\)
d)\(\frac{1}{2}.2^n+4.2^n=9.2^5\)
\(27^n:3^n=\left(27:3\right)^n=9\)
\(9^n=9\rightarrow n=1\)
\(\left(\frac{25}{5}\right)^n=5^n=5^1\)
\(\rightarrow n=1\)
\(\frac{81}{\left(-3\right)^n}=-243=\left(-3\right)^5\)
\(\rightarrow\left(-3\right)^n=81:\left(-3\right)^5=\frac{-1}{3}=\left(-3\right)^{-1}\)
\(\)
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bài 1: Tìm x,y biết rằng: x+(-frac{31}{12})^2left(frac{49}{12}right)^2-xy^2 bài 2: tìm x biết:a.5^x.left(5^3right)^2625 b.left(frac{12}{25}right)^xleft(frac{5}{3}right)^{-2}-left(-frac{3}{5}right)^4 c.left(-frac{3}{4}right)^{3x-1}frac{256}{81} d.172x^2-7^9:98^32^{-3}Bài 3: Tìm x varepsilonN biết:a.8 2^xle2^9times2^{-5} b.27 81^3:3^x 243 left(frac{2}{5}right)^xleft(frac{5}{2}right)^{-3}timesleft(-frac{2}{5}right)^2c.
Đọc tiếp
bài 1: Tìm x,y biết rằng:
\(x+(-\frac{31}{12})^2=\left(\frac{49}{12}\right)^2-x=y^2\)
bài 2: tìm x biết:
a.\(5^x.\left(5^3\right)^2=625\) b.\(\left(\frac{12}{25}\right)^x=\left(\frac{5}{3}\right)^{-2}-\left(-\frac{3}{5}\right)^4\) c.\(\left(-\frac{3}{4}\right)^{3x-1}=\frac{256}{81}\)
d.\(172x^2-7^9:98^3=2^{-3}\)
Bài 3: Tìm x \(\varepsilon\)N biết:
a.\(8< 2^x\le2^9\times2^{-5}\) b.\(27< 81^3:3^x< 243\) \(\left(\frac{2}{5}\right)^x>\left(\frac{5}{2}\right)^{-3}\times\left(-\frac{2}{5}\right)^2\)c.
Bài 1:
Ta có: \(x+\left(-\frac{31}{12}\right)^2=\left(\frac{49}{12}\right)^2-x\)
\(\Leftrightarrow2x=\frac{1440}{144}=10\)
\(\Rightarrow x=5\)
Khi đó: \(y^2=\left(\frac{49}{12}\right)^2-5=\frac{1681}{144}\)
=> \(\hept{\begin{cases}y=\frac{41}{12}\\y=-\frac{41}{12}\end{cases}}\)
Tìm tất cả các số nguyên n biết :
a, \(\frac{1}{9}=27^n=3^n\)
b, \(2^{-1}\times2^n+4\times2^n=9\times2^5\)
c, \(\left(\frac{4}{9}\right)^n=\left(\frac{3}{2}\right)^{-5}\)
d, \(\left(\frac{0}{0,125}\right)^n=128\)
tìm x thuộc N
a. \(8< 2^x< =2^9.2^{-5}\)
b .27<\(81^3\):\(3^x< 243\)
c . \(\left(\frac{2}{5}\right)^x>\left(\frac{5}{2}\right)^{-3}.\left(\frac{2}{5}\right)^2\)
a) \(8< 2^x\le2^9.2^{-5}\)
\(\Leftrightarrow2^3< x\le2^{9-5}\)
\(\Leftrightarrow2^3< 2^x\le2^4\)
\(\Leftrightarrow3< x\le4\Leftrightarrow x=4\)
b) \(27< 81^3:3^x< 243\)
\(\Leftrightarrow3^2< \left(3^4\right)^3:3^x< 3^5\)
\(\Leftrightarrow3^2< 3^{12}:3^x< 3^5\)
\(\Leftrightarrow3^2< 3^{12-x}< 3^5\)
\(\Leftrightarrow2< 12-x< 5\)
\(\Leftrightarrow\hept{\begin{cases}x=8\\x=9\end{cases}}\)
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tin so nguyen n biet rang
a)\(27^n:3^n=9\)
b)\(\frac{25}{5^n}=5\)
c)\(\frac{81}{\left(-3\right)^n}=-243\)
d)\(\frac{1}{2}.2^n+4.2^n=9.2^5\)
a) 27^n : 3^n = 9
(27 : 3)^n = 9
9^n = 9
=> n = 1
b) 25/5^n = 5
5^n = 25 : 5
5^n = 5
=> n = 1
c) 81/(-3)^n = -243
(-3)^n = -243 : 81
(-3)^n = -3
=> n = 1
d) 1/2 . 2^n + 4 . 2^n = 9 . 2^5
2^n . (1/2 + 4) = 9 . 32
2^n . 9/2 = 288
2^n = 288 : 9/2
2^n = 64
2^n = 2^6
=> n = 6
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thank you for doing your homework well !
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\(a)27^n\div3^n=9\)
\(\Rightarrow\left(27\div3\right)^n=9\)
\(\Rightarrow9^n=9\Rightarrow n=1\)
\(b)\frac{25}{5^n}=5\Rightarrow25=5^{n+1}\Rightarrow5^2=5^{n+1}\Rightarrow2=n+1\Rightarrow n=1\)
\(c)\frac{81}{\left(-3\right)^n}=-243\Rightarrow\frac{81}{\left(-3\right)^n}=\left(-3\right)^5\)
\(\Rightarrow81=\left(-3\right)^{n+5}\Rightarrow\left(-3\right)^4=\left(-3\right)^{n+5}\)
\(\Rightarrow4=n+5\Rightarrow n=-1\)
\(d)\frac{1}{2}.2^n+4.2^n=9.2^5\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)
\(\Rightarrow2^n.\frac{9}{2}=9.2^5\Rightarrow2^n=9.2^5.\frac{2}{9}\Rightarrow2^n=\frac{9.2^5.2}{9}=2^6\)
\(\Rightarrow n=6\)
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