Question

1 . Tìm x \(\in\) N , biết

a, ( 2¹⁴ : 1024 ) . 2^x = 128

b, 3^x + 3^{x +1} + 3 ^x+2 = 117

c, 2^x + 2^{x + 1} + 2^{x +2} + 2^{x + 3} = 480

d, 2³. 32 \(\ge\) 2ⁿ > 16

đ, 25 < 5ⁿ < 625

e, ( 2² : 4 ) . 2ⁿ < 32

g, 125 \(\le\) 5 . 5ⁿ \(\le\) 625

h, 16ⁿ < 32⁴

Mọi người giúp mk nha !

Answer 1

a) ta có :(2^14:1024).2^x=128

=>(2^14:2^10).2^x=2^7

=>2^4.2^x=2^7

=>2^x=2^7:2^4

=>2^x=2^3

=>x=3

b) ta có: 3^x+3^x+1+3^x+2=117

=>3^x.(1+3+3^2)=117

=>3^x.13=117

=>3^x=9=3^2

=>x=2

c)ta có 2^x+2^x+1+2^x+2+2^x+3=480

=>2^x.(1+2+2^2+2^3)=480

=>2^x.15=480

=>2^x=480:15=32=2^5

=>x=5

d) ta có: 2^3.32>=2^n>16

=>2^3.2^5>=2^>2^4

=>2^8>=2^n>2^4

=>n=8;7;6;5

còn lại tương tự

h)16^n<32^4

=>(2^4)^n<(2^5)^4

=>2^4n<2^20

=>4n<20

=>n= 0;1;2;3;4