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\(a,\frac{16}{2^n}=2\Rightarrow2^n=16:2\Rightarrow2^n=8\Rightarrow2^n=2^3\Rightarrow n=3\)
\(b,\frac{\left(-3\right)^n}{81}=-27\Rightarrow\left(-3\right)^n=81.\left(-27\right)\Rightarrow\left(-3\right)^n=-2187\Rightarrow3^n=3^7\Rightarrow n=7\)
\(c,8^n:2^n=4\Rightarrow4^n=4\Rightarrow n=1\)
\(a,\frac{16}{2^n}=2\) \(b,\frac{\left(-3\right)^n}{81}=-27\) \(c,8^n:2^n=4\)
\(\Rightarrow2^4=2^n.2\) \(\Rightarrow\left(-3\right)^n=\left(-27\right).81\) \(\Rightarrow\left(8:2\right)^n=4\)
\(\Rightarrow4=n+1\) \(\Rightarrow\left(-3\right)^n=\left(-3\right)^7\) \(\Rightarrow4^n=4\)
\(\Rightarrow n=4-1=3\) \(\Rightarrow n=7\) \(\Rightarrow n=1\)
Tìm số tự nhiên n, biết:
a) \(\frac{16}{2^n}=2\)
b) \(\frac{\left(-3\right)^n}{81}=-27\)
c) \(8^n:2^2\)
a) \(\frac{16}{2^n}=2\)
=> 16 = 2 . 2n
=> 16 = 2n+1
=> 24 = 2n+1
=> n + 1 = 4
=> n = 4 - 1
=> n = 3
Vậy n = 3
b) \(\frac{\left(-3\right)^n}{81}=-27\)
=> (-3)n = -27 . 81
=> (-3)n = (-3)3 . (-3)4
=> (-3)n = (-3)7
=> n = 7
Vậy n = 7
c) 8n : 22 = bao nhiêu vậy ban?
Chuk bn hk tốt!
a)\(\frac{16}{2^n}=2\)
\(\Rightarrow16:2=2^n\)
2n=8=23
Vậy n=3
b)\(\frac{\left(-3\right)^n}{81}=-27\)
\(\Rightarrow\)(-3)n=-27.81
(-3)n=-2187=(-3)7
Vậy n=7
c)Mk ko hiểu bn ghi gì
1.a.\(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2=\frac{17}{12}.\left(\frac{1}{20}\right)^2=\frac{17}{12}.\frac{1}{400}=\frac{17}{4800}\)
b. \(2\div\left(\frac{1}{2}-\frac{2}{3}\right)^3=2\div\left(-\frac{1}{6}\right)^3=2\div\left(-\frac{1}{216}\right)=2.\left(-216\right)=-432\)
2.a.\(\frac{16}{2^n}=2\Rightarrow2^n=16:2=8=2^3\Rightarrow n=3\)
b.\(\frac{\left(-3\right)^n}{81}=-27\Rightarrow\left(-3\right)^n=-27.81=-2187=\left(-3\right)^7\Rightarrow n=7\)
c. \(8^n:2^n=4\Rightarrow\left(8:2\right)^n=4\Rightarrow4^n=4^1\Rightarrow n=1\)
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, \(8^n:2^n=4\Leftrightarrow2^{3n}:2^n=2^2\Leftrightarrow2^{2n}=2^2\Leftrightarrow2n=2\Rightarrow n=1\)
a, \(\frac{16}{2^n}=2\Leftrightarrow2\cdot2^n=16\Leftrightarrow2^{n+1}=2^4\Leftrightarrow n+1=4\Rightarrow n=3\)
b,\(\frac{\left(-3\right)^n}{81}=-27\Leftrightarrow\left(-3\right)^n=-3^3.3^4\Leftrightarrow\left(-3\right)^n=\left(-3\right)^7\Rightarrow n=7\)
c,\(8^n:2^n=4\Leftrightarrow\left(2^3\right)^n:2^n=2^2\Leftrightarrow2^{3n}:2^{2n}=2^2\Leftrightarrow2^{3n-2n}=2^2\Leftrightarrow2^n=2^2\Leftrightarrow n=2\)
câu 1. \(\frac{16}{2^n}\)=2 =>2n=16x2=32
2n=25 => n=5
câu 2.\(\frac{\left(-3\right)^n}{81}\)=-27=33 =>(-3)n =81x33
=(-3)4x(-3)3
=(-3)7
câu 3. 8n:4n=4=>(8:4)n=4
2n=4 =22
=>n=2
\(a,\left[\left(0,5\right)^3\right]^n=\frac{1}{64}\Rightarrow\left(0,125\right)^n=0,125^2\Rightarrow n=2\)
\(b,\frac{64}{\left(-2\right)^{n+1}}=4\Rightarrow\left(-2\right)^{n+1}=\frac{64}{4}\Rightarrow\left(-2\right)^{n+1}=16\Rightarrow\left(-2\right)^{n+1}=\left(-2\right)^4\)
\(\Rightarrow n+1=4\Rightarrow n=3\)
\(c,\left(\frac{1}{3}\right)^{n+1}=\frac{1}{81}\Rightarrow\left(\frac{1}{3}\right)^{n+1}=\left(\frac{1}{3}\right)^4\Rightarrow n+1=4\Rightarrow n=3\)
\(d,\left(\frac{3}{4}\right)^n.\frac{1}{2}=\frac{81}{512}\Rightarrow\left(\frac{3}{4}\right)^n=\frac{81}{512}:\frac{1}{2}=\frac{81}{256}\Rightarrow\left(\frac{3}{4}\right)^n=\left(\frac{3}{4}\right)^4\Rightarrow n=4\)
a) \(\left(\frac{1}{3}\right)^n=\frac{1}{81}\)
\(\Rightarrow\left(\frac{1}{3}\right)^n=\frac{1^4}{3^4}\)
\(\Rightarrow\left(\frac{1}{3}\right)^n=\left(\frac{1}{3}\right)^4\)
\(\Rightarrow n=4\)
Vậy n = 4
b) \(\frac{-512}{343}=\left(\frac{-8}{7}\right)^n\)
\(\Rightarrow\frac{-8^3}{7^3}=\left(\frac{-8}{7}\right)^n\)
\(\Rightarrow\left(\frac{-8}{7}\right)^3=\left(\frac{-8}{7}\right)^n\)
\(\Rightarrow n=3\)
Vậy n = 3
\(\frac{16}{2^n}=1;2^n=8;n=3\)
\(\frac{\left(-3\right)^n}{81}=-27;\left(-3\right)^n=\left(-3\right)^7;n=7\)
\(8^n:2^n=4;\left(8:2\right)^n=4;4^n=4=4^1;n=1\)