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a) \(\left(\frac{1}{2}\right)^m=\frac{1}{32}\)
\(\Leftrightarrow\left(\frac{1}{2}\right)^m=\left(\frac{1}{2}\right)^5\)
\(\Leftrightarrow m=5\)
b) \(\frac{343}{125}=\left(\frac{7}{5}\right)^n\)
\(\Leftrightarrow\left(\frac{7}{5}\right)^3=\left(\frac{7}{5}\right)^n\)
\(\Leftrightarrow n=3\)
a)Ta có (2.5)2 = 102 =100
22.52= 4. 25=100
vì 100=100 nên (2.5)2 = 22.52
Vậy:........
Mk chỉ giúp được thế thui nha sr
a) Ta có: (2.5)2 = 6,25
22.52 = 4. 25 = 100
=> Vì 6,25 < 100 nên (2,5)2 < 22.52
a)
\(\frac{16}{2^x}=2\)
\(\Rightarrow2^{x+1}=16\)
\(\Rightarrow2^{x+1}=2^4\)
\(\Rightarrow x+1=4\)
\(\Rightarrow x=3\)
b)
\(\frac{\left(-3\right)^x}{81}=-27\)
\(\Rightarrow\left(-3\right)^x=-\left(3^3.3^4\right)\)
\(\Rightarrow-3^x=-3^7\)
=> x=7
c)
\(8^n:2^n=4\)
\(\Rightarrow2^{3n}:2^n=4\)
\(\Rightarrow2^{3n-n}=4\)
\(\Rightarrow2^{2n}=2^2\)
=>2n=2
=>n=1
a)\(\frac{16}{2^n}=2\)
=>16:2n=2
=>2n=16:2
=>2n=8
b)ko nhớ cách làm
c)8n:2n=4
=>(23)n:2n=22
=>23n:2n=22
=>23n-n=22
=>22n=22
=>2n=2
=>n=1
dc rùi chứ
A bạn ơi cho mình sửa đề một tí câu a phải là \(\dfrac{16}{2^n}=2\)
a) \(\dfrac{16}{2^n}=2\Rightarrow\dfrac{2^4}{2^n}=2\Rightarrow2^{4-n}=2\Rightarrow4-n=1\Rightarrow n=3\)
b) \(\dfrac{\left(-3\right)^n}{81}=-27\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^4}=\left(-3\right)^3\)
\(\Rightarrow\) \(\left(-3\right)^{n-4}=\left(-3\right)^3\)
\(\Rightarrow n-4=3\Rightarrow n=7\)
c) \(8^n:2^n=4=gt\Rightarrow\left(8:2\right)^n=4=gt\Rightarrow4^n=4=gt\Rightarrow n=1\)
Hok tốt nha!
a) \(\dfrac{16}{2^n}=2\)
\(\Rightarrow\)\(\dfrac{2^4}{2^n}=2\)
\(\Rightarrow\) 2. 2n = 24
2n + 1 = 24
n + 1 = 4
n = 4 - 1
n = 3
b) \(\dfrac{\left(-3\right)^n}{81}=\left(-27\right)\)
\(\Rightarrow\)\(\dfrac{\left(-3\right)^n}{\left(-3\right)^4}=\left(-3\right)^3\)
\(\Rightarrow\) (-3)n = (-3)4 . (-3)3
(-3)n = (-3)7
n = 7
c) 8n : 2n = 4
\(\Rightarrow\)(8 : 2)n = 4
4n = 4
n = 1.
a) \(\dfrac{12}{\left(-2\right)^n}=\dfrac{-12}{8}\)
\(\Rightarrow12.8=\left(-2\right)^n.\left(-12\right)\)
\(\Rightarrow96=\left(-2\right)^n.\left(-12\right)\)
\(\Rightarrow\left(-2\right)^n=\dfrac{96}{-12}\)
\(\Rightarrow\left(-2\right)^n=-8\)
\(\Rightarrow\left(-2\right)^n=\left(-2\right)^3\)
\(\Rightarrow n=3\)
Vậy \(n=3\)
2)
a) \(\dfrac{4}{9}\) và \(\dfrac{5}{8}\) Mẫu chung: 72
\(\dfrac{4}{9}=\dfrac{4.8}{72}=\dfrac{32}{72}\)
\(\dfrac{5}{8}=\dfrac{5.9}{72}=\dfrac{45}{72}\)
Vì \(\dfrac{32}{72}< \dfrac{45}{72}\)
Vậy \(\dfrac{4}{9}< \dfrac{5}{8}\)
b) \(-\sqrt{\dfrac{4}{9}}\) và \(\dfrac{-3}{4}\) MTC: 12
\(-\sqrt{\dfrac{4}{9}}=-\sqrt{\left(\dfrac{2}{3}\right)^2}=-\dfrac{2}{3}=\dfrac{-2.4}{12}=\dfrac{-8}{12}\)
\(-\dfrac{3}{4}=\dfrac{-3.3}{12}=\dfrac{-9}{12}\)
Vì \(\dfrac{-8}{12}>\dfrac{-9}{12}\)
Vậy \(-\sqrt{\dfrac{4}{9}}>\dfrac{-3}{4}\)
a) \(\frac{790^4}{79^4}=\frac{79^4.10^4}{79^4}=10^4=10000\)
b) \(\frac{3^2}{0,375^2}=\frac{0,375^2.8^2}{0,375^2}=8^2=64\)
c) \(3^2.\frac{1}{243}.81^2.\frac{1}{3^3}=3^2.3^{-5}.3^8.3^{-3}=3^2=9\)
d) \(\left(4.2^5\right):\left(2^3.\frac{1}{16}\right)=2^7:\left(2^3.2^{-4}\right)=2^7:2^{-1}=2^7:\frac{1}{2}=2^8\)
\(a;\frac{16}{2^n}=2\Leftrightarrow\frac{16}{2^n}=\frac{16}{2^3}\Rightarrow n=3\)
\(b;\frac{\left(-3\right)^n}{81}=-27\Leftrightarrow\frac{\left(-3\right)^n}{81}=\frac{\left(-3\right)^7}{81}\Rightarrow n=7\)
\(c;8^n:2^n=4\Leftrightarrow2^{3n}:2^n=2^2\Leftrightarrow2^{2n}=2^2\Rightarrow2n=2\Leftrightarrow n=1\)
a) \(\frac{16}{2^n}\)= \(2\)=> \(\frac{16}{2^n}\)= \(\frac{16}{8}\)=> 2n = 8 => 2n = 23 => n = 3.
b) Ta có : (-3)n = - 27 . 81
=> (-3)n = - 2187
=> (-3)n = (-3)7
=> n = 7
c) 8n : 2n = 4
=> 4n = 4
=> n = 1.
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