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a) Ta có: \(\left(0.125\right)^m\cdot24^m=243\)
\(\Leftrightarrow3^m=3^5\)
hay m=5
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{3}^{2n-1}=243\)
\(< =>\frac{1}{3}^{n+n}=\frac{243}{3}=81\)
\(< =>\frac{1}{3^{n+n}}=81\)
\(< =>81.3^n.3^n=1\)
\(< =>3^{2n}=\frac{1}{81}\)
\(< =>3^{2n}=3^{-4}\)
\(< =>x=-2\)
Bài làm:
a) \(\left(\frac{1}{3}\right)^{2n-1}=243\)
\(\Leftrightarrow3^{1-2n}=3^5\)
\(\Rightarrow1-2n=5\)
\(\Leftrightarrow2n=-4\)
\(\Rightarrow n=-2\)
b) \(\left(0,125\right)^{n+1}=64\)
\(\Leftrightarrow\left(\frac{1}{8}\right)^{n+1}=8^2\)
\(\Rightarrow-n-1=2\)
\(\Rightarrow n=-3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có : (x - 4)2 = (x - 4)4
=> (x - 4)4 - (x - 4)2 = 0
=> (x - 4)2.[(x - 2)2 - 1] = 0
=> \(\orbr{\begin{cases}\left(x-4\right)^2=0\\\left(x-4\right)^2-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x-4=0\\\left(x-4\right)^2=1\end{cases}}\)
Nếu x - 4 = 0 => x = 4
Nếu (x - 4)2 = 1 => \(\orbr{\begin{cases}x-4=1\\x-4=-1\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x=3\end{cases}}\)
Vậy \(x\in\left\{3;4;5\right\}\)
2) a. Bạn xem lại đề
b) Ta có : 85n : 17n= 625
=> (85 :17)n = 625
=> 5n = 625
=> 5n = 53
=> n = 3
Vậy n = 3
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 32 < 2n < 128
25 < 2n < 27
=> 2n = 26
=> n = 6
Vậy n = 6
b) 9 . 27 \(\le\) 3n \(\le\)243
=> 243 \(\le\)3n \(\le\)243
=> 35 \(\le\)3n \(\le\)35
=> 3n = 35
=> n = 5
Vậy n = 5
Ủng hộ mk nha !!! ^_^
\(\left(\dfrac{1}{8}\right)^m\cdot24^m=243\)
\(\Rightarrow\left(\dfrac{1}{8}\cdot24\right)^m=243\)
\(\Rightarrow3^m=243=3^5\)
\(\Rightarrow m=5\)
(0,125)m . 24m = 243
(0,125 . 24)m =243
3m =35
=>m = 5