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a)\(\left(\dfrac{1}{2}\right)^n=\dfrac{1}{32}\)
=>\(\left(\dfrac{1}{2}\right)^n=\left(\dfrac{1}{2}\right)^5\)
=>n=5
b)\(\left(\dfrac{343}{125}\right)=\left(\dfrac{7}{5}\right)^n\)
=>\(\left(\dfrac{7}{5}\right)^3=\left(\dfrac{7}{5}\right)^n\)
=>n=3
c)\(\dfrac{16}{2^n}=2\)
=>2n=\(\dfrac{16}{2}\)
=>2n=8
=>2n=23
=>n=3
d)\(\dfrac{\left(-3\right)^n}{81}=-27\)
=>(-3)n=-27.81
=>(-3)n=-2187
=>(-3)n=(-3)7
=>n=7
e)8n:2n=4
=>(23)n:2n=4
=>23n:2n=4
=>23n-n=4
=>22n=4
=>22n=22
=>2n=2
=>n=1
f)32.3n=35
=>3n=35:32
=>3n=35-2
=>3n=33
=>n=3
g) (22:4).2n=4
=>1.2n=22
=>n=2
h)3-2.34.3n=37
=>\(\left(\dfrac{1}{3}\right)^2\).34.3n=37
=>32.3n=37
=>32+n=37
=>2+n=7
=>n=5
Bài 1:
a: \(\left(2x-1\right)^4=16\)
=>2x-1=2 hoặc 2x-1=-2
=>2x=3 hoặc 2x=-1
=>x=3/2 hoặc x=-1/2
b: \(\left(2x-y+7\right)^{2012}+\left|x-3\right|^{2013}< =0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-y+7=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=2x+7=y=2\cdot3+7=13\end{matrix}\right.\)
c: \(10800=2^4\cdot3^3\cdot5^2\)
mà \(2^{x+2}\cdot3^{x+1}\cdot5^x=10800\)
nên \(\left\{{}\begin{matrix}x+2=4\\x+1=3\\x=2\end{matrix}\right.\Leftrightarrow x=2\)
a, \(\left(4.2\right)^5:\left(2^3.\dfrac{1}{16}\right)=8^5:\left(2^3.\dfrac{1^4}{2^4}\right)=\left(2^3\right)^5:\dfrac{2^3.1^4}{2^4}=2^{15}:\dfrac{1}{2}=2^{15}.2=2^{16}\)
\(b,\dfrac{2^2.4.32}{2^2.2^5}=\dfrac{2^2.2^4.2^5}{2^2.2^5}=2^4=16\)
\(a,\dfrac{\left(4.2\right)^5}{2^3.\dfrac{1}{16}}=\dfrac{\left(2^3\right)^5}{2^3.2^{-4}}=\dfrac{2^{15}}{2^{-1}}=2^{16}\)
b,\(\dfrac{2^2.4.32}{2^2.2^5}=\dfrac{2^2.2^2.2^5}{2^2.2^5}=2^2=4\)
Số tự nhiên n thỏa mãn:22.32n.\(\left(\frac{2}{3}\right)^n\).2n=82944 là..............(kết quả thôi)