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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!
Bạn 12345678901 xuống lớp 1 học đạo đức làm người nhé bạn. Lịch sự tí đi
a: \(=3^2\cdot3^3\cdot3^{-4}\cdot3^2=3^{2+3-4+2}=3^3\)
b: \(=2^2\cdot2^5:\left(2^3\cdot\dfrac{1}{2^4}\right)=2^7:\dfrac{1}{2}=2^8\)
c: \(=9\cdot32\cdot\dfrac{4}{9}=128=2^7\)
d: \(=\dfrac{1}{27}\cdot3^4=3^1\)
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
a) \(\left(\frac{1}{3}\right)^n=\frac{1}{27}\)
\(\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^3\)
\(\Rightarrow n=3\)
b) \(\left(\frac{3}{5}\right)^n=\frac{81}{625}\)
\(\left(\frac{3}{5}\right)^n=\left(\frac{3}{5}\right)^4\)
\(\Rightarrow n=4\)
c) \(3^n\cdot2^n=36\)
\(\left(3\cdot2\right)^n=36\)
\(6^n=6^2\)
\(\Rightarrow n=2\)
d) \(\frac{2^n}{3^n}=\frac{8}{27}\)
\(\left(\frac{2}{3}\right)^n=\left(\frac{2}{3}\right)^3\)
\(\Rightarrow n=3\)
h) \(8< 2^n\le2^9.2^{-5}\Leftrightarrow2^3< 2^n\le2^4\) \(\Rightarrow3< n\le4\)
Vì n là số tự nhiên nên n = 4
k) \(27< 81^3:3^n< 243\Leftrightarrow3^3< 3^{12-n}< 3^5\Rightarrow3< 12-n< 5\Leftrightarrow7< n< 9\)
Vì n là số tự nhiên nên n = 8
l) \(\left(5n+1\right)^2=\frac{36}{49}\Leftrightarrow\left(5n+1\right)^2=\left(\frac{6}{7}\right)^2\Rightarrow5n+1=\frac{6}{7}\) (vì n là số tự nhiên)
=> n = -1/35 (không tm)
m) \(\left(n-\frac{2}{9}\right)^3=\left(\frac{2}{3}\right)^6\Leftrightarrow\left(n-\frac{2}{9}\right)^3=\left(\frac{4}{9}\right)^3\Rightarrow n-\frac{2}{9}=\frac{4}{9}\Leftrightarrow n=\frac{2}{3}\left(ktm\right)\)
n) \(\left(8n-1\right)^{2m+1}=5^{2m+1}\Leftrightarrow8n-1=5\Leftrightarrow n=\frac{3}{4}\left(ktm\right)\) (cần thêm đk của m)
h)
\(8< 2^2\le2^9.2^{-5}\)
\(\Rightarrow2^3< 2^n\le2^4\)
\(\Rightarrow2^n=2^4\Rightarrow n=4\)
\(\frac{1}{2}.2^n+4.2^n=9.2^5\Rightarrow2^n\left(\frac{1}{2}+4\right)=288\Rightarrow2^n.\frac{9}{2}=288\Rightarrow2^{n-2}.9=288\Rightarrow2^{n-2}=32\)(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......
~~~~~~~~~~~~~~~
a)27n:3n=9
(27:3)n=9
9n=91
n=1
Vậy n=1
b)\(\left(\frac{25}{5}\right)^n=5\)
\(5^n=5^1\)
n=1
Vạy n=1
c)\(\left(-\frac{81}{3}\right)^n=-243\)
\(\left(-27\right)^n=\left(-3\right)^5\)
\(\left[\left(-3\right)^3\right]^n=\left(-3\right)^5\)
\(\left(-3\right)^{3n}=\left(-3\right)^5\)
\(3n=5\)
\(n=\frac{5}{3}\)
Vậy \(n=\frac{5}{3}\)
d)\(\frac{1}{2}.2^n+4.2^n=9.5^n\)
\(2^n.\left(\frac{1}{2}+4\right)=9.5^n\)
\(2^n.\frac{9}{2}=3^2.5^n\)