Câu hỏi của Phạm Mỹ Duyên

Question

So sánh : 201^60 và 398^45
(bằng phương pháp so sánh lũy thừa trung gian)

Kiều Vũ Linh · Accepted Answer

$201^{60}=\left(201^4\right)^{15}=1944810000^{15}$

$398^{45}=\left(398^3\right)^{15}=63044792^{15}$

Do $1944810000>63044792$

$\Rightarrow1944810000^{15}>63044792^{15}$

$\Rightarrow201^{60}>398^{45}$

Câu trả lời:

$201^{60}=\left(201^4\right)^{15}=1944810000^{15}$

$398^{45}=\left(398^3\right)^{15}=63044792^{15}$

Do $1944810000>63044792$

$\Rightarrow1944810000^{15}>63044792^{15}$

$\Rightarrow201^{60}>398^{45}$

Nguyễn Nhân Dương · Answer

Ta có:

$201^{60}>200^{60};398^{45}< 400^{45}$

$200^{60}=\left(2.100\right)^{60}=2^{60}.100^{60}=2^{60}.\left(10^2\right)^{60}$

$=2^{60}.10^{120}=2^{60}.10^{30}.10^{90}$

$400^{45}=\left(2.100\right)^{45}=2^{45}.100^{45}=2^{45}.\left(10^2\right)^{45}$

$=2^{45}.10^{90}$

Mà $2^{60}.10^{30}.10^{90}>2^{45}.10^{90}$

$\Rightarrow200^{60}>400^{45}$

$\Rightarrow201^{60}>200^{60}>400^{45}>398^{45}$

$\Rightarrow201^{60}>398^{45}$

Câu trả lời:

Ta có:

$201^{60}>200^{60};398^{45}< 400^{45}$

$200^{60}=\left(2.100\right)^{60}=2^{60}.100^{60}=2^{60}.\left(10^2\right)^{60}$

$=2^{60}.10^{120}=2^{60}.10^{30}.10^{90}$

$400^{45}=\left(2.100\right)^{45}=2^{45}.100^{45}=2^{45}.\left(10^2\right)^{45}$

$=2^{45}.10^{90}$

Mà $2^{60}.10^{30}.10^{90}>2^{45}.10^{90}$

$\Rightarrow200^{60}>400^{45}$

$\Rightarrow201^{60}>200^{60}>400^{45}>398^{45}$

$\Rightarrow201^{60}>398^{45}$