6.2-bo'lim: Logarifm funktsiyalari

1-3-masalalar uchun ifodani logarifmik shaklda yozing.

1. \({7^5} = 16807\) Yechim
2. \({16^{\frac{3}{4}}} = 8\) Yechim
3. \({\left( {\displaystyle \frac{1}{3}} \right)^{ - 2}} = 9\) Yechim

4-6-masalalar uchun ifodani eksponensial shaklda yozing.

1. \({\log _2}\,32 = 5\) Yechim
2. \({\log _{\frac{1}{5}}}\,\displaystyle \frac{1}{{625}} = 4\) Yechim
3. \({\log _9}\,\displaystyle \frac{1}{{81}} = - 2\) Yechim

7-12-masalalar uchun kalkulyatordan foydalanmasdan har birining aniq qiymatini aniqlang.

1. \({\log _3}81\) Yechim
2. \({\log _5}125\) Yechim
3. \({\log _2}\displaystyle \frac{1}{8}\) Yechim
4. \({\log _{\frac{1}{4}}}16\) Yechim
5. \(\ln {{\bf{e}}^4}\) Yechim
6. \(\log \displaystyle \frac{1}{{100}}\) Yechim

13-15-masalalar uchun quyida keltirilganlarning har birini oddiyroq logarifmlar bilan yozing

1. \(\log \left( {3{x^4}{y^{ - 7}}} \right)\) Yechim
2. \(\ln \left( {x\sqrt {{y^2} + {z^2}} } \right)\) Yechim
3. \({\log _4}\left( {\displaystyle \frac{{x - 4}}{{{y^2}\,\sqrt[5]{z}}}} \right)\) Yechim

16 - 18 muammolar uchun quyidagi koeffitsienti bitta bo'lgan bitta logarifmga birlashtiring.

1. \(2{\log _4}x + 5{\log _4}y - \frac{1}{2}{\log _4}z\) Yechim
2. \(3\ln \left( {t + 5} \right) - 4\ln t - 2\ln \left( {s - 1} \right)\) Yechim
3. \(\displaystyle \frac{1}{3}\log a - 6\log b + 2\) Yechim

19 va 20-masalalar uchun asosiy formulani o'zgartirish va quyidagi har birining qiymatini topish uchun kalkulyatordan foydalaning.

1. \({\log _{12}}35\) Yechim
2. \({\log _{\frac{2}{3}}}53\) Yechim

21-23-masalalar uchun berilgan funksiyalarning har birini chizing.

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