Tính: \(\left(0,125\right)^m\times24^m=243\)
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a,\(\left(\dfrac{1}{3}\right)^{2n-1}=243\)
\(\Rightarrow\left(\dfrac{1}{3}\right)^{2n-1}=\left(\dfrac{1}{3}\right)^{-5}\)
Vì \(\dfrac{1}{3}\ne\pm1;\dfrac{1}{3}\ne0\) nên
\(2n-1=-5\Rightarrow2n=-4\Rightarrow n=-2\)
Vậy........
b, \(\left(0,125\right)^{n+1}=64\)
\(\Rightarrow\left(\dfrac{1}{8}\right)^{n+1}=\left(\dfrac{1}{8}\right)^{-2}\)
Vì \(\dfrac{1}{8}\ne\pm1;\dfrac{1}{8}\ne0\) nên
\(n+1=-2\Rightarrow n=-3\)
Vậy..........
Chúc bạn học tốt!!!
a) Ta có: \(\left(\dfrac{1}{3}\right)^{2n-1}=243\Rightarrow\left(3^{-1}\right)^{2n-1}=3^5\)
\(\Rightarrow3^{-2n+1}=3^5\)
Suy ra: \(-2n+1=5\Rightarrow-2n=4\Rightarrow n=-2\)
b) \(\left(0,125\right)^{n+1}=64\Rightarrow\left(\dfrac{1}{8}\right)^{n+1}=8^2\)
\(\Rightarrow\left(8^{-1}\right)^{n+1}=8^2\)
\(\Rightarrow8^{-n-1}=8^2\)
Suy ra: \(-n-1=2\Rightarrow n=-3\)
Hok tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
\(M=\sqrt{\left(\frac{1}{25}\right)^{\left(-\frac{3}{2}\right)}-\left(\frac{1}{8}\right)^{\left(-\frac{2}{3}\right)}}=\sqrt{\left(5^{-2}\right)^{-\frac{3}{2}}-\left(2^{-3}\right)^{-\frac{2}{3}}}=\sqrt{5^3-2^2}=\sqrt{121}=11\)
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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)
a.
\(\left(\frac{1}{3}\right)^{2x-1}=243\)
\(\left(\frac{1}{3}\right)^{2x-1}=\left(\frac{1}{3}\right)^{-5}\)
\(2x-1=-5\)
\(2x=-5+1\)
\(2x=-4\)
\(x=-\frac{4}{2}\)
\(x=-2\)
b.
\(\left(0,125\right)^{x+1}=64\)
\(\left(0,125\right)^{x+1}=\left(0,125\right)^{-2}\)
\(x+1=-2\)
\(x=-2-1\)
\(x=-3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) c1:
(8 x 24) : 4
=8 x (24 : 4)
=8 x 6
=48
c2:
(8 x 24) : 4
=192 : 4
=48
b) c1
(15 x 24) : 6
=360 : 6
=60
c2:
(15 x 24) : 6
=15 x (24 : 6)
=15 x 4
=60
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\dfrac{1}{8}\right)^m\cdot24^m=243\)
\(\Rightarrow\left(\dfrac{1}{8}\cdot24\right)^m=243\)
\(\Rightarrow3^m=243=3^5\)
\(\Rightarrow m=5\)
(0,125)m . 24m = 243
(0,125 . 24)m =243
3m =35
=>m = 5
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\dfrac{1}{3}\right)^x+\left(\dfrac{1}{3}\right)^{x+2}=\dfrac{10}{243}\)
\(\left(\dfrac{1}{3}\right)^x+\left(\dfrac{1}{3}\right)^x.\left(\dfrac{1}{3}\right)^2=\dfrac{10}{243}\)
\(\left(\dfrac{1}{3}\right)^x.\left[1+\left(\dfrac{1}{3}\right)^2\right]=\dfrac{10}{243}\)
\(\left(\dfrac{1}{3}\right)^x.\dfrac{10}{9}=\dfrac{10}{243}\)
\(\left(\dfrac{1}{3}\right)^x=\dfrac{10}{243}:\dfrac{10}{9}\)
\(\left(\dfrac{1}{3}\right)^x=\dfrac{1}{27}\)
\(\left(\dfrac{1}{3}\right)^x=\left(\dfrac{1}{3}\right)^3\)
\(\Rightarrow x=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\dfrac{3^5}{-\left(0.003\right)^3\cdot0.09}=-10^{11}\)
=>\(\left(0,125\cdot4\right)^m=243\)
=>\(3^m=243\)
Mà \(3^5=243\)
=>\(m=5\)