Asosiy tarkibga o'tish

6.2-bo'lim : Logarifm funktsiyalari

1-5-masalalar uchun ifodani logarifmik shaklda yozing.

  1. \(\displaystyle {11^{ - 3}} = \frac{1}{{1331}}\)
  2. \({4^7} = 16384\)
  3. \({\left( {\displaystyle \frac{2}{7}} \right)^{ - 3}} =\displaystyle \frac{{343}}{8}\)
  4. \({25^{\,\frac{3}{2}}} = 125\)
  5. \({27^{ - \,\,\frac{5}{3}}} =\displaystyle \frac{1}{{243}}\)

6-10-masalalar uchun ifodani eksponensial shaklda yozing.

  1. \({\log _{\frac{1}{6}}}\,36 = - 2\)
  2. \({\log _{12}}\,20736 = 4\)
  3. \({\log _9}\,243 =\displaystyle \frac{5}{2}\)
  4. \(\displaystyle {\log _4}\,\frac{1}{{128}} = - \frac{7}{2}\)
  5. \({\log _8}\,32768 = 5\)

11-18-masalalar uchun kalkulyatordan foydalanmasdan har birining aniq qiymatini aniqlang.

  1. \({\log _7}343\)
  2. \({\log _4}1024\)
  3. \({\log _{\frac{3}{8}}}\displaystyle \frac{{27}}{{512}}\)
  4. \({\log _{11}}\displaystyle \frac{1}{{121}}\)
  5. \({\log _{0.1}}0.0001\)
  6. \({\log _{16}}4\)
  7. \(\log 10000\)
  8. \(\ln \displaystyle \frac{1}{{\sqrt[5]{{\bf{e}}}}}\)

19-20-masalalar uchun quyida keltirilgan har birini oddiyroq logarifmlar bilan yozing

  1. \({\log _7}\left( {10{a^7}{b^3}{c^{ - 8}}} \right)\)
  2. \(\log \left[ {{z^2}{{\left( {{x^2} + 4} \right)}^3}} \right]\)
  3. \(\ln \left( {\displaystyle \frac{{{w^2}\,\sqrt[4]{{{t^3}}}}}{{\sqrt {t + w} }}} \right)\)

22-24-masalalar uchun har birini bitta koeffitsientli bitta logarifmga birlashtiring.

  1. \(7\ln t - 6\ln s + 5\ln w\)
  2. \(\displaystyle \frac{1}{2}\log \left( {z + 1} \right) - 2\log x - 4\log y - 3\log z\)
  3. \(2{\log _3}\left( {x + y} \right) + 6{\log _3}x - \displaystyle \frac{1}{3}\)

25 va 26-masalalar uchun asosiy formulani o'zgartirish va quyidagi har birining qiymatini topish uchun kalkulyatordan foydalaning.

  1. \({\log _7}100\)
  2. \({\log _{\frac{5}{7}}}\displaystyle \frac{1}{8}\)

27-31-masalalar uchun berilgan funksiyalarning har birini chizing.

  1. \(g\left( x \right) = \ln \left( { - x} \right)\)
  2. \(g\left( x \right) = \ln \left( {x - 3} \right)\)
  3. \(g\left( x \right) = \ln \left( x \right) + 7\)
  4. \(g\left( x \right) = \ln \left( {x + 2} \right) - 4\)
  5. \(g\left( x \right) = \ln \left( {x - 6} \right) + 2\)