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24 tháng 9 2017

a) \(\dfrac{1}{9}.27^n=3^n\)

\(\Leftrightarrow\dfrac{1}{9}=3^n:27^n\)

\(\Leftrightarrow\dfrac{1}{9}=\left(\dfrac{3}{27}\right)^n\)

\(\Leftrightarrow\dfrac{1}{9}=\left(\dfrac{1}{9}\right)^n\)

\(\Leftrightarrow n=1\)

b) \(3^{-2}.3^4.3^n=3^7\)

\(\Leftrightarrow3^2.3^n=3^7\)

\(\Leftrightarrow3^n=3^7:3^2\)

\(\Leftrightarrow3^n=3^5\)

\(\Leftrightarrow n=5\)

c) \(32^{-n}.16^n=2048\)

\(\Leftrightarrow\left(2^5\right)^{-n}.\left(2^4\right)^n=2^{11}\)

\(\Leftrightarrow2^{-5n}.2^{4n}=2^{11}\)

\(\Leftrightarrow2^{-n}=2^{11}\)

\(\Leftrightarrow n=-11\)

17 tháng 2 2016

a)\(\frac{1}{3^2}\cdot3^{3n}=3^n\Rightarrow3=3^{3n-2}=3^n\Rightarrow3n-2=n\Rightarrow n=1\)

b)\(\frac{1}{3^2}\cdot3^4\cdot3^n=3^7\Rightarrow3^{n+2}=3^7\Rightarrow n+2=7\Rightarrow n=5\)

13 tháng 12 2017

a) \(2010^{100}+\)\(2010^{99}=2010^{99}.2010+2010^{99}.1=2010^{99}.\left(2010+1\right)=2010^{99}.2011\)Vậy biểu thức chia hết cho 2011.

a: \(5^3\cdot25^n=5^{3n}\)

\(\Leftrightarrow5^{3n}=5^3\cdot5^{2n}\)

=>3n=2n+3

hay n=3

b: \(a^{\left(2n+6\right)\left(3n-9\right)}=1\)

=>(2n+6)(3n-9)=0

=>n=-3 hoặc n=3

c: \(\dfrac{1}{3}\cdot3^n=7\cdot3^2\cdot3^4-2\cdot3^n\)

\(\Leftrightarrow3^n\cdot\dfrac{1}{3}+3^n\cdot2=7\cdot3^6\)

\(\Leftrightarrow3^n=3^7\)

hay n=7

16 tháng 7 2018

\(a)A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

\(A=\dfrac{2^{12}.3^5-\left(2^2\right)^63.\left(3^2\right)^2}{\left(2^2\right)^6.3^6+\left(2^3\right)^4.3^5}-\dfrac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3\right)^3.7^3+5^9.\left(7.2\right)^3}\)

\(A=\dfrac{2^{12}.3^5-2^{12}.3^5}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^6.7^3+5^9.7^3.2^3}\)

\(A=\dfrac{0}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3\left(1-7\right)}{5^6.7^3\left(1+5^3+2^3\right)}\)

\(A=0-\dfrac{5^4.\left(-6\right)}{1+125+8}\)

\(A=0-\dfrac{625.\left(-6\right)}{134}\)

\(A=\dfrac{-3750}{134}\)\(=\dfrac{-1875}{67}\)

\(b)3^{n+2}-2^{n+2}+3^n-2^n\)

\(=3^n.3^2-2^n.2^2+3^n-2^n\)

\(=(3^n.9+3^n)-\left(2^n.4+2^n\right)\)

\(=3^n.10-2^n.5\)

\(=3^n.10-2^{n-1}.10\)

\(=10\left(3^n-2^{n-1}\right)⋮10\)

\(Suy\) \(ra:\) \(3^{n+2}-2^{n+2}+3^n-2^n⋮10\)

16 tháng 7 2018

b. Ta có: \(3^{n +2}-2^{n+2}+3^n-2^n\)

\(=\left(3^{n+2}+3^n\right)-\left(2^{n+2}+2^n\right)\)

\(=\left(3^n.3^2+3^n\right)-\left(2^{n-1}.2^3+2^{n-1}.2\right)\)

\(=3^n.\left(3^2+1\right)-2^{n-1}\left(2^3+2\right)\)

\(=3^n.10-2^{n-1}.10⋮10\)

24 tháng 8 2019

a) \(\frac{1}{9}.27^n=3^n\)

\(\Leftrightarrow3^{-2}.3^{3n}=3^n\)

\(\Leftrightarrow3^{3n-2}=3^n\)

\(\Leftrightarrow3n-2=n\)

\(\Leftrightarrow2n=2\)

\(\Leftrightarrow n=1\)

24 tháng 8 2019

b)\(3^{-2}.3^4.3^n=3^7\)

\(\Leftrightarrow3^{2+n}=3^7\)

\(\Leftrightarrow2+n=7\)

\(\Leftrightarrow n=5\)

18 tháng 7 2018

a)\(\dfrac{1}{9}.27^n=3^n\)

<=>27n=3n:\(\dfrac{1}{9}\)

<=>27n:3n=\(\dfrac{1}{9}\)

<=>33n:3n=\(\dfrac{1}{9}\)

<=>32n=\(\dfrac{1}{9}\)

<=>9n=\(\dfrac{1}{9}\)

<=>9n+1=1

<=>n+1=0

<=>n=-1

vậy n=-1