81^7-27^9-9^13 chia hết cho 45
Ta có: 81^7-27^9-9^13
=(3^4)^7-(3^3)^9-(3^2)^13
=3^28-3^27-3^26
=3^26.(3^2-3-1)
=3^26.5
=3^13. 3^2 .5
=3^13.45
Vì 45 chia hết cho 45 ⇒ 3^13.45 chia hết cho 45
hay 81^7-27^9-9^13
Vậy............
Bài 43
a,27<3^x<3.81 b,32≤ 2^x ≤ 2^2x-3.2^8-2x
3^3<3^x<3^5 2^5≤2^x≤2^2x-3+8-2x ⇒x=4(t/m) 2^5≤2^x≤2^5
Vậy..... ⇒x=5(t/m)
Vậy............
c,4^15.9^15<2^x.3^x<18^16.2^16
36^15<6^x<36^16
(6^2)^15<6^x<(6^2)^16
6^30<6^x<6^32
⇒x=31(t/m)
Vây.........
d, 2^x+1.3^y=12x
2^x+1.3y=2^2x.3x
⇒x+1=2x ⇒x=1(t/m)
y=x y=1(t/m)
Vậy........
e, 6^x:2^2000=3y
2^x.3^x:2^2000=3y
2^x-2000=3^y-x
Ta có 3^y-x luôn lẻ mà 2^x-2000 chỉ lẻ khi x-2000=0
⇒x=2000
Khi đó 3^y-x=2^x-2000=1
⇒y-x=0
⇒y=x=2000(t/m)
Vậy.....
f, (2x-1)^6=(2x-1)^8
⇔ (2x-1)^6-(2x-8)=0
⇔(2x-1)^6.[1-(2x-1)^2]=0
⇔ (2x-1)^6=0 ⇔2x=1 ⇔x=1/2(t/m)
1-(2x-1)^2=0 2x-1=1 x=1(t/m)
Vậy...........
