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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
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. \(\Rightarrow5^2<5^{n-1}<5^4\)
\(\Rightarrow n-1=3\)
\(\Rightarrow n=4\).
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) \(x=\frac{2}{3}\)
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
Bài 3: Tìm x:
a. \(\left(2x-1\right)^4=81\)
\(\Rightarrow\left(2x-1\right)^4=3^4\)
=> 2x - 1 = 3
=> 2x = 4
=> x = 2
b. \(\left(x-2\right)^2=1\)
\(\Rightarrow\) \(\left(x-2\right)^2=1^2\)
=> x - 2 = 1
=> x = 3
c. \(x^{2000}=x\)
=> x = 1
d. \(\left(4x-3\right)^3=-125\)
\(\Rightarrow\left(4x-3\right)^3=\left(-5\right)^3\)
=> 4x - 3 = -5
=> 4x = -2
=> x = \(\dfrac{-1}{2}\)
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,\(5^{-1}\times25^n=125 \)
= \(\frac{1}{5}\times25^n=125\)
= \(25^n=125\div\frac{1}{5}\)
= \(25^n=625\)
= \(25^n=25^2\)
\(\Rightarrow n=2\)