Tomsk State Pedagogical University Bulletin
RU EN






Today: 25.12.2025
Home Issues 2015 Year Issue №1 METHODIC TECHNIQUES FOR SOLVING EQUATIONS CONTAINING THE UNKNOWN AT THE BASE AND INDEX
  • Home
  • Current Issue
  • Bulletin Archive
    • 2025 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2024 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2023 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2022 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2021 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2020 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 2019 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
    • 2018 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
    • 2017 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2016 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2015 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2014 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2013 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
      • Issue №13
    • 2012 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
      • Issue №13
    • 2011 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
      • Issue №13
    • 2010 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2009 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2008 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
    • 2007 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
    • 2006 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
      • Issue №10
      • Issue №11
      • Issue №12
    • 2005 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
    • 2004 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
    • 2003 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
    • 2002 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
    • 2001 Year
      • Issue №1
      • Issue №2
      • Issue №3
    • 2000 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
      • Issue №8
      • Issue №9
    • 1999 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
      • Issue №7
    • 1998 Year
      • Issue №1
      • Issue №2
      • Issue №3
      • Issue №4
      • Issue №5
      • Issue №6
    • 1997 Year
      • Issue №1
      • Issue №2
      • Issue №3
  • Search
  • Rating
  • News
  • Editorial Board
  • Information for Authors
  • Review Procedure
  • Information for Readers
  • Editor’s Publisher Ethics
  • Contacts
  • Manuscript submission
  • Received articles
  • Accepted articles
  • Subscribe
  • Service Entrance
vestnik.tspu.ru
praxema.tspu.ru
ling.tspu.ru
npo.tspu.ru
edujournal.tspu.ru

TSPU Bulletin is a peer-reviewed open-access scientific journal.

E-LIBRARY (РИНЦ)
Ulrich's Periodicals Directory
Google Scholar
European reference index for the humanities and the social sciences (erih plus)
Search by Author
- Not selected -
  • - Not selected -
Яндекс.Метрика

METHODIC TECHNIQUES FOR SOLVING EQUATIONS CONTAINING THE UNKNOWN AT THE BASE AND INDEX

Apaycheva L.A., Shuvalova L.E.

Information About Author:

The article is devoted to the solutions to the equations containing the unknown at the base and index. A detailed analysis of the problem proved that there is no decisive answer as to what conditions need to be imposed on the equation function. The primary way of solving such equations is taking the logarithm of both members of the equation, in this case some roots are lost. It should be noted that equations of such type are studied at school and pupils are to master the skills of solution to such equations. The article suggests algorythm of solution of these equations, analyses certain examples. The conclusions are drawn that solving such equations can greatly contribute to the development of students’ logical thinking as well as their abilities, intuition and cognitive power.

Keywords: power function, equation root, acceptable region, complex exponent

References:

1. Kolesnikova S. I. Matematika. Reshenie slozhnykh zadach Edinogo gosudarstvennogo ekzamena [Mathematics. The complex problems solution of the uniform state examinations]. 3th ed. Moscow, Ayris-press Publ., 2007. 272 p. (in Russian).

2. Potapova M. K., Olehnik S. N., Nesterenko Yu. V. Konkursnyye zadachi po matematike. Spravochnoe posobiye [Competitive problems in mathematics. The handbook]. Moscow, Stoletie Publ., 1995. 544 p. (in Russian).

3. Tkachuk V. V. Matematika-abiturientu [Mathematics for a university entrant]. Moscow, MTSNMO Publ., 2004. 922 p. (in Russian).

4. Matematicheskiy entsiklopedicheskiy slovar’ [Encyclopedic Dictionary of Mathematics]. Moscow, Sovetskaya Entsiklopediya Publ., 1988. 848 p. (in Russian).

5. Skanavi M. I. (Ed.). Sbornik konkursnykh zadach po matematike dlya postupayushchikh vo vtuzy [The competitive problems workbook in mathematics for university entrants]. St. Petersburg, 1994. 516 p. (in Russian).

6. Mazur K. I. Reshebnik vsekh konkursnykh zadach po matematike sbornika pod redaktsiey M. I. Skanavi [The solution of all competitive problems in mathematics collection edition by Skanavi M. I.]. 2th ed. Kiev, Ukrainskaya entsyklopediya M. P. Bazhan Publ., 1994. 279 p. (in Russian).

7. Kravtsev S. V., Makarov Yu. N., Maksimov M. I., Naralenkov M. I., Chirskiy V. G. Metody resheniya zadach po algebre: ot prostykh do samykh slozhnykh [Methods of problems solution in algebra: from easy to the most diffi cult]. Мoscow, Examen Publ., 2001. 544 p. (in Russian).

8. Vukulova T. M., Potapov M. K., Shevkin A. V. Ob uravneniyakh vida f(x)(x) = g(x) [About equations of a form f(x)(x) = g(x)]. Mathematics in the school, 2008, no. 7, pp. 37–40 (in Russian).

9. Nelin E. P. Algebra i nachala analiza: Dvukhurovnevyy uchebnik dlya 10 kl. obshcheobrazovat. ucheb. zavedeniy [Algebra and analysis beginnings: The two-level textbook for 10 classes of comprehensive schools]. Translated from Ukrainian by Nelin E. P. Kharkov, Mir detstva Publ., 2006. 448 p. (in Russian).

10. Makuseva T. G., Yakovleva E. V. Ispol’zovanie logicheskikh zadach v protsese samostoyatel’noi raboty studentov [Logic problems using in the independent work students course]. Vestnik Tomskogo gosudarstvennogo pedagogicheskogo universiteta – TSPU Bulletin, 2010, vol. 12, pp. 102–104 (in Russian).

apajcheva_l._a._51_54_1_154_2015.pdf ( 452.38 kB ) apajcheva_l._a._51_54_1_154_2015.zip ( 445.77 kB )

Issue: 1, 2015

Series of issue: Issue 1

Rubric: TEACHING NATURAL SCIENCES

Pages: 51 — 54

Downloads: 1459

For citation:


2025 Tomsk State Pedagogical University Bulletin

Development and support: Network Project Laboratory TSPU