1.8-bo'lim : Logarifm funktsiyalari

Kalkulyatordan foydalanmasdan, quyidagi har birining aniq qiymatini aniqlang.

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

Quyidagilarning har birini oddiyroq logarifmlar shaklida 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. \(\displaystyle \ln \left( {\frac{{{w^2}\,\sqrt[4]{{{t^3}}}}}{{\sqrt {t + w} }}} \right)\)

Quyidagilarning har birini bitta koeffitsientli bitta logarifmaga 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. \(\displaystyle 2{\log _3}\left( {x + y} \right) + 6{\log _3}x - \frac{1}{3}\)

Quyidagilarning har birining qiymatini topish uchun asosiy formulani o'zgartirish va kalkulyatordan foydalaning.

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