Quod Erat Demonstrandum


用 logarithm 計出頭幾個位

Filed under: HKCEE,mathematics — johnmayhk @ 12:05 下午
Tags: ,

昨天匆匆出了份中四 logarithm 的習作,其中一題:

Find the first digit of 1997^{2009}.



但直接用會「爆機」的,我們要 Take log。

x = 1997^{2009},則

\log x = 2009\log 1997 \approx 6630.459532(這是計算機顯示的答案)


6630.459532 < \log x < 6630.459533

10^{6630.459532} < x < 10^{6630.459533}
10^{6630 + 0.459532} < x < 10^{6630 + 0.459533}
10^{0.459532} \times 10^{6630} < x < 10^{0.459533} \times 10^{6630}
2.880925316 \times 10^{6630} < x < 2.88093195 \times 10^{6630}(用計算機得出的)

可見,1997^{2009} = 28809...(共 6631 個位)


6 則迴響 »

  1. Hi,

    An interesting article. HK maths is really challenging to the mind.

    Wen Shih

    迴響 由 Wen Shih — 2009/05/14 @ 6:00 上午 | 回應

  2. Thank you Wen Shih, your comments are really encouraging!

    I found your website


    is really great for mathematics learning, thank you for your work!

    You are a mathematics educator in Singapore, what do you think about the mathematics learning and teaching (especially in secondary level) in your country? I just had a very vague idea on “TLLM" (Teach Less Learn More), what an ideal slogan! Is it really ‘workable’?

    Thank you again!

    迴響 由 johnmayhk — 2009/05/14 @ 10:40 上午 | 回應

  3. Hi John,

    Thanks for your encouragement :)

    I used to teach in a junior college but I left in Aug ’06 to further my study. From Jan ’07 to the present, I teach part-time at the National Institute of Education.

    My personal experience with TLLM is limited so I cannot comment much about its effectiveness. However, the A-level students that I teach feel that the way their schools are doing TLLM can be improved upon so that they can learn better and more meaningfully. The TLLM approach that I tend to hear often from these students is to make use of the school’s e-learning website where students are to download a set of notes/worksheets to carry out self-study.


    Wen Shih

    迴響 由 Wen Shih — 2009/05/14 @ 5:29 下午 | 回應

    • Dear Wen Shih,

      Thank you for your sharing.

      I do agree that if students could use resources in the internet appropriately, they should obtain much better than merely from mathematics lessons in school.

      The new education system (so-called ‘334’ system) will be implemented in the coming academic year here in Hong Kong. It is still doubtful to me whether the new education reform could empower Hong Kong students to be more ‘competitive’ or not. Teachers are told to change their teaching style (or role) so as to fit the needs of students. And, of course, education is a also big business to make money, many had already seized the chance.

      Best Regards,

      JOHN NG

      迴響 由 johnmayhk — 2009/05/15 @ 11:18 下午 | 回應

  4. Hi John,

    Thanks for sharing the development of education in HK. There will be hiccups to be expected and these will need to be ironed out in the initial implementation to allow all involved (education policy makers, educators and students) to learn valuable experience to improve the system.

    I feel that policy makers should go to the ground often and ask students what they really need, rather than focus on staying ahead and specifying the ‘supposed’ needs (and then taking them to be real needs of students) to achieve it.

    When I ask my students what they need, the typical response is better quality teaching that emphasises understanding, clarity, simplicity and meaning of concepts and skills.

    Thanks and have a nice weekend!

    Wen Shih

    迴響 由 Wen Shih — 2009/05/16 @ 1:14 下午 | 回應

  5. Hi,

    If one seeks only to make money out of education, then he/she is not a true educator.


    Wen Shih

    迴響 由 Wen Shih — 2009/05/16 @ 1:17 下午 | 回應

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