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靈意壹零死死 2019-12-14 08:29 AM

指數大小

Which of the following numbers is the greatest?
A. 1000^9000
B. 2000^8000
C. 3000^7000
D. 4000^6000


Solve the question without using calculator, thank you 

hoyh 2019-12-14 01:59 PM

Consider using common logarithm .........

愛純情 2019-12-21 10:00 PM

[quote]原帖由 [i]靈意壹零死死[/i] 於 2019-12-14 08:29 AM 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=511711519&ptid=28754398][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]
Which of the following numbers is the greatest?
A. 1000^9000
B. 2000^8000
C. 3000^7000
D. 4000^6000


Solve the question without using calculator, thank you  [/quote]
A. 1000^9000 = 1 x 10^3^9000 = 1 x 10^27000
B. 2000^8000 = 2 x 10^3^8000 = 2 x 10^24000
C. 3000^7000 = 3 x 10^3^7000 = 3 x 10^21000
D. 4000^6000 = 4 x 10^3^6000 = 4 x 10^18000
Therefore, A is the greatest

辟易愛我 2020-2-14 01:06 PM

[quote]原帖由 [i]愛純情[/i] 於 2019-12-21 10:00 PM 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=512063371&ptid=28754398][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]

A. 1000^9000 = 1 x 10^3^9000 = 1 x 10^27000
B. 2000^8000 = 2 x 10^3^8000 = 2 x 10^24000
C. 3000^7000 = 3 x 10^3^7000 = 3 x 10^21000
D. 4000^6000 = 4 x 10^3^6000 = 4 x 10^18000
Therefore, A is the greatest ... [/quote]

我是數學新手,
請教是不是10^的指數, 例如3和9000, 是可以乘在一起, 成為一個總指數?

其實想請教,
把9000變成27000,
或把8000變24000,
變了之後, 與變之前有甚麼分別?足以用來作為辨識出誰是最大。
其實會不會不倍大,也一樣是9000這個指數最大。
意思是, 可不可以一眼看出, 不用計?
既然已經最大, 即是有很多零, 所以即使4x 也不會大過1x,
因為有很多指數?

hoyh 2020-2-15 04:03 PM

[quote]原帖由 [i]愛純情[/i] 於 2019-12-21 10:00 PM 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=512063371&ptid=28754398][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]

A. 1000^9000 = 1 x 10^3^9000 = 1 x 10^27000
B. 2000^8000 = 2 x 10^3^8000 = 2 x 10^24000
C. 3000^7000 = 3 x 10^3^7000 = 3 x 10^21000
D. 4000^6000 = 4 x 10^3^6000 = 4 x 10^18000
Therefore, A is the greatest ... [/quote]
A. 1000^9000 = [color=#ff0000]([/color]1 x 10^3[color=#ff0000])[/color]^9000 = 1 x 10^27000
B. 2000^8000 = [color=#ff0000]([/color]2 x 10^3[color=#ff0000])[/color]^8000 = (2[color=#ff0000]^8000[/color]) x (10^24000)
C. 3000^7000 = [color=#ff0000]([/color]3 x 10^3[color=#ff0000])[/color]^7000 = (3[color=#ff0000]^7000[/color]) x (10^21000)
D. 4000^6000 = [color=#ff0000]([/color]4 x 10^3[color=#ff0000])[/color]^6000 = (4[color=#ff0000]^6000[/color]) x (10^18000)
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