Question

[Hoàng Khánh Linh]

so sánh 5^2n+2 với 3^3n+3

Answer 1

[❖×✔ᴍê ʜọᴄ)ミ★ ❖(☂TΣΔM☂STUDIΣS☂)ミ★]

32n32n vàvà 23n23n (n∈N∗)(n∈N∗)

32n=(32)n=9n32n=(32)n=9n 

23n=(23)n=8n23n=(23)n=8n 

Vì 8 <9Vì 8 <9

⇒8n<9n⇒8n<9n hayhay 23n<32n23n<32n

VậyVậy 23n<32n23n<32n

Answer 2

[Cao Tùng Lâm]

$3^{2n}$ $\text{và}$ $2^{3n}$ $(n\in N\ast )$

$3^{2n}=(3^2{)}^n=9^n$ 

$2^{3n}=(2^3{)}^n=8^n$ 

$\text{Vì 8 <9}$

$\Rightarrow 8^n<9^n$ $\text{hay}$ $2^{3n}<3^{2n}$

$\text{Vậy}$ $2^{3n}<3^{2n}$