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a, \(\frac{16}{2^n}=2\Leftrightarrow16=2^n.2\Rightarrow2^4=2^{n+1}\Rightarrow n+1=4\Rightarrow n=3\)
b) \(\frac{\left(-3\right)^n}{81}=-27\Rightarrow\left(-3\right)^n=-27.81\Rightarrow\left(-3\right)^n=-3^3.3^4\Rightarrow\left(-3\right)^n=\left(-3\right)^7\Rightarrow n=7\)
c, \(8^n:2^n=4\Leftrightarrow2^{3n}:2^n=2^2\Leftrightarrow2^{2n}=2^2\Leftrightarrow2n=2\Rightarrow n=1\)
\(\frac{16}{2^n}=1;2^n=8;n=3\)
\(\frac{\left(-3\right)^n}{81}=-27;\left(-3\right)^n=\left(-3\right)^7;n=7\)
\(8^n:2^n=4;\left(8:2\right)^n=4;4^n=4=4^1;n=1\)
Qùa tặng cuộc sống(1 bài)
a) 16 = 2,2n
24 = 2n+1
4 = n+1 => n = 3
a) \(\frac{\left(-3\right)^n}{81}=-27\)
\(\Rightarrow\left(-3\right)^n=-2187\)
\(\Rightarrow\left(-3\right)^n=\left(-3\right)^7\)
\(\Rightarrow n=7\)
Vậy \(n=7\)
b) \(8^n:2^n=4\)
\(8^n:2^n=4^1\)
mà \(8:2=4\)
\(\Rightarrow n=1\)
Vậy \(n=1\)
a, \(\dfrac{16}{2^n}=2\)
\(2^n=\dfrac{16}{2}\)
\(2^n=8\)
\(2^n=2^3\)
=> n = 3
b, \(\dfrac{\left(-3\right)^n}{81}=-27\)
\(\left(-3\right)^n=-27\cdot81\)
\(\left(-3\right)^n=\left(-3\right)^3\cdot3^4\)
\(\left(-3\right)^n=\left(-3\right)^7\)
=> n = 7
c, \(8^n:2^n=4\)
\(2^{3n}:2^n=2^2\)
\(2^{2n}=2^2\)
=> 2n = 2
n = 2:2
n = 1
a )
\(\dfrac{16}{2^n}=2\) \(\Leftrightarrow16:x=2\)
\(\Rightarrow x=8\)
\(2^n=8\Rightarrow n=3\)
b )
\(\dfrac{\left(-3\right)^n}{81}=-27\) \(\Leftrightarrow x=-27.81\)
\(\Rightarrow x=-2187\)
\(\left(-3\right)^n=-2187\Rightarrow n=7\)
c )
\(8^n:2^n=4\Leftrightarrow4^n=4\)
\(\Rightarrow n=1\)
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!
\(a,\frac{16}{2^n}=2\Rightarrow2^n=16:2\Rightarrow2^n=8\Rightarrow2^n=2^3\Rightarrow n=3\)
\(b,\frac{\left(-3\right)^n}{81}=-27\Rightarrow\left(-3\right)^n=81.\left(-27\right)\Rightarrow\left(-3\right)^n=-2187\Rightarrow3^n=3^7\Rightarrow n=7\)
\(c,8^n:2^n=4\Rightarrow4^n=4\Rightarrow n=1\)
\(a,\frac{16}{2^n}=2\) \(b,\frac{\left(-3\right)^n}{81}=-27\) \(c,8^n:2^n=4\)
\(\Rightarrow2^4=2^n.2\) \(\Rightarrow\left(-3\right)^n=\left(-27\right).81\) \(\Rightarrow\left(8:2\right)^n=4\)
\(\Rightarrow4=n+1\) \(\Rightarrow\left(-3\right)^n=\left(-3\right)^7\) \(\Rightarrow4^n=4\)
\(\Rightarrow n=4-1=3\) \(\Rightarrow n=7\) \(\Rightarrow n=1\)
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