6.2-bo'lim : Logarifm funktsiyalari
10. Kalkulyatordan foydalanmasdan \({\log _{\frac{1}{4}}}16\) ning aniq qiymatini aniqlang.
Maslahat: Esda tutingki, logarifmni eksponensial shaklga o'tkazish ko'pincha bunday logarifmalarni baholashga yordam beradi.
Yechim
Logarifmni eksponensial shaklga o'tkazish,
\[{\log _{\frac{1}{4}}}16 = ?\hspace{0.25in} \Rightarrow \hspace{0.25in}{\left( {\frac{1}{4}} \right)^?} = 16\]2-qadam
Endi bilamizki, kasrni darajaga olib, butun sonni chiqarsak, manfiy ko'rsatkichga ega bo'lishimiz kerak. Endi biz \({4^2} = 16\) ekanligini ham bilamiz. Shuning uchun biz \({\left( {\frac{1}{4}} \right)^{ - 2}} = {\left( {\frac{4}{1}} \right)^2} = 16\) ekanligini ko'rishimiz mumkin va shuning uchun bizda bo'lishi kerak,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{{{\log }_{\frac{1}{4}}}16 = - 2}}\]