1) 3^1994+4^1993-3^1992
= 3^1992.(9+3-1)=3^1992.11 chia hết cho 11
=> 3^1994+3^1993-3^1992 chia hết cho 11
B2
a)2^n =4.32=128=2^7
=>n=7
b)3^3n.3^2n =9^25
=>3^5n=3^50 =>n=10
bn có thể giải chi tuêts hơn đc ko , mk ko hỉu
1) Chứng minh
a) \(3^{1994}+3^{1993}-3^{1992}⋮11\)
Giải
Ta có : \(3^{1994}+3^{1993}-3^{1992}\)
\(=3^{1992}.\left(3^2+3-1\right)\)
\(=3^{1992}.11⋮11\)
\(\Rightarrow3^{1994}+3^{1993}-3^{1992}⋮11\left(\text{đpcm}\right)\)
b) 413 + 325 - 88 \(⋮\)5
Giải
Ta có : \(4^{13}+32^5-8^8=\left(2^2\right)^{13}+\left(2^5\right)^5-\left(2^3\right)^8\)
\(=2^{2.13}+2^{5.5}-2^{3.8}\)
\(=2^{26}+2^{25}-2^{24}\)
\(=2^{14}.\left(2^2+2-1\right)\)
\(\Rightarrow2^{14}.5⋮5\)
=> 413 + 325 - 88 \(⋮\)5 (ĐPCM)
2) Tìm n biết :
\(a)\frac{2^n}{32}=4\)
\(\Rightarrow\frac{2^n}{2^5}=2^4\)
\(\Rightarrow2^n=2^5.2^4\)
\(\Rightarrow2^n=2^9\)
\(\Rightarrow n=9\)
b) \(27^n.9^n=9^{27}:81\)
\(\Rightarrow\left(27.9\right)^n=9^{27}:9^2\)
\(\Rightarrow\left(3^3.3^2\right)^n=9^{29}\)
\(\Rightarrow3^{5n}=\left(3^2\right)^{29}\)
\(\Rightarrow3^{5n}=3^{58}\)
\(\Rightarrow5n=58\)
\(\Rightarrow n=\frac{58}{5}\)
1.Chứng minh
a) 3^{1994}+3^{1993}-3^{1992}⋮1131994+31993−31992⋮11
giải
Ta có : 3^{1994}+3^{1993}-3^{1992}31994+31993−31992
=3^{1992}.\left(3^2+3-1\right)=31992.(32+3−1)
=3^{1992}.11⋮11=31992.11⋮11
\Rightarrow3^{1994}+3^{1993}-3^{1992}⋮11\left(\text{đpcm}\right)⇒31994+31993−31992⋮11(đpcm)
b) 413 + 325 - 88 ⋮⋮5
Giải
Ta có : 4^{13}+32^5-8^8=\left(2^2\right)^{13}+\left(2^5\right)^5-\left(2^3\right)^8413+325−88=(22)13+(25)5−(23)8
=2^{2.13}+2^{5.5}-2^{3.8}=22.13+25.5−23.8
=2^{26}+2^{25}-2^{24}=226+225−224
=2^{14}.\left(2^2+2-1\right)=214.(22+2−1)
\Rightarrow2^{14}.5⋮5⇒214.5⋮5
=> 413 + 325 - 88 ⋮⋮5 (ĐPCM)
2 Tìm .n biết :
a)\frac{2^n}{32}=4a)322n=4
\Rightarrow\frac{2^n}{2^5}=2^4⇒252n=24
\Rightarrow2^n=2^5.2^4⇒2n=25.24
\Rightarrow2^n=2^9⇒2n=29
\Rightarrow n=9⇒n=9
b) 27^n.9^n=9^{27}:8127n.9n=927:81
\Rightarrow\left(27.9\right)^n=9^{27}:9^2⇒(27.9)n=927:92
\Rightarrow\left(3^3.3^2\right)^n=9^{29}⇒(33.32)n=929
\Rightarrow3^{5n}=\left(3^2\right)^{29}⇒35n=(32)29
\Rightarrow3^{5n}=3^{58}⇒35n=358
\Rightarrow5n=58⇒5n=58
\Rightarrow n=\frac{58}{5}⇒n=558
