Question

[Bùi Ngọc Anh]

1 .Tìm y ∈ N biết

a. 9 < 3^y < 81

b. 25 ≤ 5^y ≤ 125

c. 16 ≤ 4^y ≤ 1024

2. Tìm y ∈ N biết

a. 3 x 2^y = 48

b. 5 x y⁷ = 640

c . y¹⁰⁰ = y²

d. ( y - 3 )⁵ = 243

e. ( 2y + 1 )³ = 125

i. 2^y+3 + 2^y = 288

Các bạn giải ra ( cách làm ) giúp mình nhé .

Cảm ơn nhiều !

Answer 1

[Anh Nguyendieu]

1.

a. 9 < \(^{3^y}\)< 81

9=3\(^{^2}\)

81=3\(^{^4}\)

\(\Rightarrow\)y=3 vì \(3^2< 3^3< 3^4\)

b.25\(\le\)5\(^{^y}\)\(\le\)125

25=5\(^{^2}\)

125=5\(^{^3}\)

\(\Rightarrow\)y=2 và 3 vì 5\(^{^2}\)\(\le\)5\(^{^2}\)(5\(^{^3}\))\(\le\)5\(^{^3}\)

c.

16\(\ge\)4\(^{^y}\)\(\ge\)1024

16=4\(^{^2}\)

1024=4\(^{^5}\)

\(\Rightarrow\)y=2,3,4,5 vì 4​​\(^{^2}\)​​​\(\ge\)4\(^{^2\left(4^3;4^4;4^5\right)}\)

\(^{^2}\)

\(\Rightarrow\)

Answer 2

[Anh Nguyendieu]

2.

a.3x\(^{2^y}\)=48

\(^{2^y}\)=48:3

\(^{2^y}\)=16

\(\Rightarrow\)y=4 vì \(^{2^4}\)=16

b.5x\(y^7\)=640

\(y^7\)=640:5

\(y^7\)=128

\(\Rightarrow\)y=2 vì \(2^7\)=128

c.\(y^{100}\)=\(y^2\)

\(\Rightarrow\)y=1 vì:

\(1^{100}\)=1

\(1^2\)=1

d.(y-3)\(^{^5}\)=243

\(\Rightarrow\)y-3=3 vì 3\(^{^5}\)=243

y=3+3

y=6

e.(2y+1)\(^{^3}\)=125

\(\Rightarrow\)2y+1=5 vì 5\(^{^3}\)=125

2y=5-1=4

y=4:2=2

i.2\(^{^{y+3}}\)+2\(^{^y}\)=288

2\(^{^y}\).2\(^{^3}\)+2\(^{^y}\)=288

2\(^{^y}\).2\(^{^3}\)=288-2\(^{^y}\)

2\(^{^y}\).8=288-2\(^{^y}\)

8=(288-2\(^{^y}\)):2\(^{^y}\)

8=288:2\(^{^y}\)-2\(^{^y}\):2\(^{^y}\)

8=288:2\(^{^y}\)-1

288:2\(^{^y}\)=8+1=9

2\(^{^y}\)=288:9=32

\(\Rightarrow\)y=5 vì 2\(^{^5}\)=32