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a) \(9.27^n=3^5\Rightarrow3^2.\left(3^3\right)^n=3^5\)
\(\Rightarrow3^2.3^{3n}=3^5\Rightarrow3^{5n}=3^5\)
\(\Rightarrow5n=5\Rightarrow n=1\)
b)\(\left(2^3:4\right).2^n=4\Rightarrow\left(2^3:2^2\right).2^n=2^2\)
\(\Rightarrow2.2^n=2^2\Rightarrow2^{1+n}=2^2\)
\(\Rightarrow1+n=2\Rightarrow n=1\)
c)\(3^2.3^4.3^n=3^7\Rightarrow3^{6+n}=3^7\)
\(\Rightarrow6+n=7\Rightarrow n=1\)
d)\(2^{-1}.2^n+4.2^n=9.2^5\)
\(\Rightarrow2^n\left(2^{-1}+4\right)=3^2.2^5\)
\(\Rightarrow\)\(2^n\left(\frac{1}{2}+4\right)=3^2.2^5\)
\(\Rightarrow\)\(2^n.\frac{3^2}{2}=3^2.2^5\)
\(\Rightarrow\)\(2^{n-1}.3^2=3^2.2^5\)
\(\Rightarrow n-1=5\Rightarrow n=6\)
e)\(243\ge3^n\ge9.3^2\)
\(\Rightarrow3^5\ge3^n\ge3^2.3^2\)
\(\Rightarrow3^5\ge3^n\ge3^4\)
\(\Rightarrow5\ge n\ge4\Rightarrow5;4\)
f)\(2^{n+3}.2^n=128\)
\(\Rightarrow2^{n+3+n}=2^7\)
\(\Rightarrow2^{2n+3}=2^7\)
\(\Rightarrow2n+3=7\Rightarrow2n=4\Rightarrow n=2\)
Hok tối
a: \(\Leftrightarrow3^n:27^n=\dfrac{1}{9}\)
\(\Leftrightarrow\left(\dfrac{1}{9}\right)^n=\dfrac{1}{9}\)
hay n=1
b: \(\Leftrightarrow3^n\cdot3^2=3^8\)
=>n+2=8
hay n=6
c: \(\Leftrightarrow2^n\cdot\dfrac{9}{2}=9\cdot2^5\)
\(\Leftrightarrow2^n=2^6\)
hay n=6
d: \(\Leftrightarrow8^n=512\)
hay n=3
Bài 3: Tìm x:
a. \(\left(2x-1\right)^4=81\)
\(\Rightarrow\left(2x-1\right)^4=3^4\)
=> 2x - 1 = 3
=> 2x = 4
=> x = 2
b. \(\left(x-2\right)^2=1\)
\(\Rightarrow\) \(\left(x-2\right)^2=1^2\)
=> x - 2 = 1
=> x = 3
c. \(x^{2000}=x\)
=> x = 1
d. \(\left(4x-3\right)^3=-125\)
\(\Rightarrow\left(4x-3\right)^3=\left(-5\right)^3\)
=> 4x - 3 = -5
=> 4x = -2
=> x = \(\dfrac{-1}{2}\)
c, \(\frac{-32}{-2^n}=4\)
\(\Rightarrow-2^n=-32:4\)
\(\Rightarrow-2^n=-8\)
\(\Rightarrow-2^n=-2^3\Rightarrow n=3\)
d, \(\frac{8}{2^n}=2\)
\(\Rightarrow2^n=8:2\)
\(\Rightarrow2^n=4\)
\(\Rightarrow2^n=2^2\Rightarrow n=2\)
e, \(\frac{25^3}{5^n}=25\)
\(\Rightarrow5^n=25^3:25\)
\(\Rightarrow5^n=25^2\)
\(\Rightarrow5^n=5^4\Rightarrow n=4\)
i , \(8^{10}:2^n=4^5\)
\(\Rightarrow2^n=8^{10}:4^5\)
\(\Rightarrow2^n=\left(2^3\right)^{10}:\left(2^2\right)^5\)
\(\Rightarrow2^n=2^{30}:2^{10}\)
\(\Rightarrow2^n=2^{20}\Rightarrow n=20\)
k, \(2^n.81^4=27^{10}\)
\(\Rightarrow2^n=27^{10}:81^4\)
\(\Rightarrow2^n=\left(3^3\right)^{10}:\left(3^4\right)^4\)
\(\Rightarrow2^n=3^{30}:3^{16}\)
\(\Rightarrow2^n=3^{14}\)
\(\Rightarrow2^n=4782969\)Không chia hết cho 2 nên ko có Gt n thỏa mãn
mình làm 1 câu lm mẫu thôi nhé
a) \(2.16\ge2^n>4\)
\(\Rightarrow2.2^4\ge2^n>2^2\)
\(\Rightarrow2^5\ge2^n>2^2\)
\(\Rightarrow5\ge n>2\)
\(\Rightarrow n=5;4;3\)
tíc mình nha
Cái này tag tên tú hay ace cũng được mà:
Đặt+ sưả đề:
\(A=1+2+2^2+2^3+.....+2^{2004}+2^{2005}\)
\(2A=2\left(1+2+2^2+2^3+.....+2^{2004}+2^{2005}\right)\)
\(2A=2+2^2+2^3+2^4+.....+2^{2005}+2^{2006}\)
\(2A-A=\left(2+2^2+2^3+2^4+.....+2^{2005}+2^{2006}\right)-\left(1+2+2^2+2^3+.....+2^{2004}+2^{2005}\right)\)\(A=2^{2006}-1\)
Tìm chữ số tận cùng:
a;b dễ tự làm nha
c) \(19^n+5n+1890^n\)
Xét:
n lẻ:
\(\Rightarrow19^n=\overline{....9}\)
\(\Rightarrow5n=\overline{....5}\)
\(\Rightarrow1980^n=\overline{....0}\)
\(\Leftrightarrow19^n+5n+1980^n=\overline{...9}+\overline{...5}+\overline{...0}=\overline{...4}\)
Xét: n chẵn:
\(\Rightarrow19^n=\overline{....1}\)
\(\Rightarrow5n=\overline{...0}\)
\(\Rightarrow1890^n=\overline{...0}\)
\(\Leftrightarrow19^n+5n+1980^n=\overline{...1}+\overline{...0}+\overline{...0}=\overline{...1}\)
\(2^{4n}+1\)
\(4n⋮4\)
Nên ta sẽ xét những số mũ chia hết cho 4
\(2^{1.4}=2^4=\overline{...6}\)
\(2^{2.4}=2^8=\overline{...6}\)
\(2^{3.4}=2^{12}=\overline{...6}\)
\(\Rightarrow2^{4n}=\overline{...6}\)
\(\Rightarrow2^{4n}+1=\overline{...7}\)
a ) \(125.5\ge5^n\ge5.25\Rightarrow5^4\ge5^n\ge5^3\)
=> n { 4 ; 3 }
b ) \(243\ge3^n\ge9.27\Rightarrow3^5\ge3^n\ge3^5\)
=> n { 5 }
c ) \(8.16\ge2^n\ge4\Rightarrow2^7\ge2^n\ge2^2\)
=> n { 7 ; 6 ; 5 ; 4 ; 3 ; 2 }
d ) 2n+3 . 2n = 144
=> 2 (n +3 )+ n = 144