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a)
\(2^n=16\Rightarrow n=4\)
b)
\(4^n=4096\Rightarrow n=6\)
c)
\(6^{n+3}=216\Rightarrow n=0\)
d)
\(3^n=243\Rightarrow n=5\)
e)
\(5^n=15625\Rightarrow n=6\)
f)
\(4^n=1024\Rightarrow n=5\)
a) Ta có: \(256< 2^n< 1024\)
\(\Leftrightarrow2^8< 2^n< 2^{10}\)
\(\Rightarrow8< n< 10\)
\(\Rightarrow n=10\)
Vậy \(n=10\)
b) Ta có: \(27< 3^n< 243\)
\(\Leftrightarrow3^3< 3^n< 3^5\)
\(\Rightarrow3< n< 5\)
\(\Rightarrow n=4\)
Vậy \(n=4\)
c) Ta có: \(16< 4^n< 256\)
\(\Leftrightarrow4^2< 4^n< 4^4\)
\(\Rightarrow2< n< 4\)
\(\Rightarrow n=3\)
Vậy \(n=3\)
d) Ta có: \(125< 5^n< 3125\)
\(\Leftrightarrow5^3< 5^n< 5^5\)
\(\Rightarrow3< n< 5\)
\(\Rightarrow n=4\)
Vậy n=4
a) \(256< 2^n< 1024\)
Ta có : \(2^8< 2^n< 2^{10}\)
Vậy n = 9
b) \(27< 3^n< 243\)
Ta có : \(3^3< 3^n< 3^5\)
Vậy n = 4
c) \(16< 4^n< 256\)
Ta có : \(4^2< 4^n< 4^4\)
Vậy n = 3
d) \(125< 5^n< 3125\)
Ta có : \(5^3< 5^n< 5^5\)
Vậy n = 4
a) 27. 3n=243. 3n
=243:27
=9. có 3n
=9=32.
=>3n=32. => n=2.
a)
\(3^4.3^n:9=3^7\)
\(\Rightarrow3^4.3^n=3^7.9\)
\(\Leftrightarrow3^4.3^n=3^7.3^2\)
\(\Rightarrow3^4.3^n=3^9\)
\(\Rightarrow3^n=3^9:3^4\)
\(\Rightarrow3^n=3^5\)
\(\Rightarrow n=5\)
Vậy \(n=5\)
d)
\(2^n:4=16\)
\(\Leftrightarrow2^n:2^2=2^4\)
\(\Rightarrow2^n=2^4.2^2\)
\(\Rightarrow2^n=2^6\)
\(\Rightarrow n=6\)
Vậy \(n=6\)
a) \(2^n:4=16\)
\(2^n:2^2=2^4\)
\(=>n-2=4\)
\(=>n=6\)
b) \(3^n:3^2=243\)
\(3^n:3^2=3^5\)
\(=>n-2=5\)
\(=>n=7\)
vay \(n=7\)
c) \(2^n-64=2^6\)
\(2^n-2^6=2^6\)
\(2^n=2^6+2^6\)
\(2^n=128\)
\(2^n=2^7\)
\(=>n=7\)
vay \(n=7\)
a) \(15+2^n=31\)
\(2^n=16\Rightarrow n=4\)
b) \(2.2^n+4.2^n=6.2^5\)
\(2^n\left(2+4\right)=6.2^5\)
\(2^n.6=6.2^5\Rightarrow n=5\)
c) \(32^n:16^n=1024\)
\(\left(2^5\right)^n:\left(2^4\right)^n=2^{10}\)
\(2^{5n}:2^{4n}=2^{10}\)
\(2^n=2^{10}\Rightarrow n=10\)
d) \(5^n+5^{n+2}=650\)
\(5^n+5^n.25=650\)
\(5^n\left(1+25\right)=650\)
\(5^n.26=650\)
\(5^n=25\Rightarrow n=2\)
e) \(3^n+5.3^{n+1}=432\)
\(3^n+5.3^n.3=432\)
\(3^n\left(1+15\right)=432\)
\(3^n.16=432\)
\(3^n=27\Rightarrow n=3\)
\(a,3^2\cdot3^4\cdot3^n=3^{12}\)
\(\Rightarrow3^{6+n}=3^{12}\)
\(\Rightarrow6+n=12\)
\(\Rightarrow n=6\)
\(b,2^n:4=16\)
\(\Rightarrow2^n:2^2=2^4\)
\(\Rightarrow2^{n-2}=2^4\)
\(\Rightarrow n-2=4\)
\(\Rightarrow n=6\)
\(c,6\cdot2^n+3\cdot2^n=9\cdot2^9\)
\(\Rightarrow2^n\left(6+3\right)=9\cdot2^9\)
\(\Rightarrow2^n\cdot9=9\cdot2^9\)
\(\Rightarrow2^n=2^9\)
\(\Rightarrow n=9\)
a>2^n=16=>2^n=2^4 =>n=4
3^n=243=> 3^n=3^5 =>n=5
b>4^n=4096 =>4^n=4^6=>n=6
5^n=15625 =>5^n=5^6 =>n=6
c>6^n+3=216 =. 6^n+3=6^3 =>n+3=3
n=0
4^n-1=1024 =>4^n-1=4^5 =>n-1=5
n=4
Chuc ban vao nam hoc dc nhieu may man!!