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a. \(\Rightarrow5^{-1}.5^{2n}=5^3\)
\(\Rightarrow5^{2n-1}=5^3\)
=> 2n-1=3
=> 2n=4
=> n=2
b. \(\Rightarrow3^{n-1}+6.3^{n-1}=7.3^6\)
\(\Rightarrow\left(1+6\right).3^{n-1}=7.3^6\)
\(\Rightarrow7.3^{n-1}=7.3^6\)
=> n-1=6
=> n=7
c. \(\Rightarrow3^4<3^{-2}.3^{3n}<3^{10}\)
\(\Rightarrow3^4<3^{3n-2}<3^{10}\)
\(\Rightarrow3n-2\in\left\{5;6;7;8;9\right\}\)
\(\Rightarrow3n\in\left\{7;8;9;10;11\right\}\)
\(\text{Mà n là số nguyên}\Rightarrow n=3\).
d. \(\Rightarrow5^2<5^{n-1}<5^4\)
\(\Rightarrow n-1=3\)
\(\Rightarrow n=4\).
| x - 1 | + | x + 3 | = 3 ( * )
xét : x - 1 = 0 => x = 1
x + 3 = 0 => x = -3
x - 1 < 0 => x < 1
x + 3 < 0 => x < -3
x - 1 > 0 => x > 1
x + 3 > 0 => x > -3
Lập bảng xét dấu,ta có :
x -3 1
x+3 - 0 + | +
x-1 - | - 0 +
nếu x < -3 thì * <=> : ( 1 - x ) + ( -3 - x ) = 3
1 - x + ( -3 ) - x = 3
-2x = 5
x = -5/2 ( loại )
nếu -3 \(\le\)x < 1 thì * <=> : ( 1 - x ) + ( x + 3 ) = 3
1 - x + x + 3 = 3
0x = -1 ( ko có GT x thỏa mãn )
nếu x \(\ge\)1 thì * <=> : ( x -1 ) + ( x + 3 ) = 3
x - 1 + x + 3 = 3
2x = 1
x = 1/2 ( ko có GT x thỏa mãn )
Vậy ko có GT x nào thỏa mãn bài trên.
a) 25 < 5n:5 < 625
52 < 5n:5 < 54
2 < n:5 < 4
=> n : 5 = 3
=> n = 15
b) 34 < \(\frac{1}{9}.27^n\)< 310
34 < \(\frac{27^n}{9}\)< 310
34 < 33n-2 < 310
=> 3n - 2 \(\in\) { 5 ; 6 ; 7 ; 8 ; 9 }
Nếu 3n - 2 = 5 thì n = 7/3 ( loại )
Nếu 3n - 2 = 6 thì n = 8/3 ( loại )
Nếu 3n - 2 = 7 thì n = 3 ( thỏa mãn )
Nếu 3n - 2 = 8 thì n = 10/3 ( loại )
Nếu 3n - 2 = 9 thì n = 11/3 ( loại )
Vậy n = 3
Bài 2:
a: =>50x+50=0
=>50x=-50
=>x=-1
b: \(\Leftrightarrow5^{2x-1}=5^3\)
=>2x-1=3
=>2x=4
=>x=2
c: \(\Leftrightarrow3^{x-1}+6\cdot3^{x-1}=7\cdot3^6\)
=>3^x-1=3^6
=>x-1=6
=>x=7
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
c, \(\frac{-32}{-2^n}=4\)
\(\Rightarrow-2^n=-32:4\)
\(\Rightarrow-2^n=-8\)
\(\Rightarrow-2^n=-2^3\Rightarrow n=3\)
d, \(\frac{8}{2^n}=2\)
\(\Rightarrow2^n=8:2\)
\(\Rightarrow2^n=4\)
\(\Rightarrow2^n=2^2\Rightarrow n=2\)
e, \(\frac{25^3}{5^n}=25\)
\(\Rightarrow5^n=25^3:25\)
\(\Rightarrow5^n=25^2\)
\(\Rightarrow5^n=5^4\Rightarrow n=4\)
i , \(8^{10}:2^n=4^5\)
\(\Rightarrow2^n=8^{10}:4^5\)
\(\Rightarrow2^n=\left(2^3\right)^{10}:\left(2^2\right)^5\)
\(\Rightarrow2^n=2^{30}:2^{10}\)
\(\Rightarrow2^n=2^{20}\Rightarrow n=20\)
k, \(2^n.81^4=27^{10}\)
\(\Rightarrow2^n=27^{10}:81^4\)
\(\Rightarrow2^n=\left(3^3\right)^{10}:\left(3^4\right)^4\)
\(\Rightarrow2^n=3^{30}:3^{16}\)
\(\Rightarrow2^n=3^{14}\)
\(\Rightarrow2^n=4782969\)Không chia hết cho 2 nên ko có Gt n thỏa mãn
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) \(x=\frac{2}{3}\)
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!
a, 5-1x 25n = 125 d, 25 < 5n:5 < 625
5-1 x 52n = 53 52 < 5n:5 < 54
=> -1+2n=3 => n=4
=>2n = 3--1
=>2n=4
=>n =2
a,\(5^{-1}\times25^n=125 \)
= \(\frac{1}{5}\times25^n=125\)
= \(25^n=125\div\frac{1}{5}\)
= \(25^n=625\)
= \(25^n=25^2\)
\(\Rightarrow n=2\)