Buning uchun tabiiy logarifmadan yoki umumiy logarifmadan foydalanishimiz mumkin, shuning uchun ikkalasini ham bajaramiz.

\[{\log _{\frac{2}{3}}}53 = \frac{{\ln 53}}{{\ln \frac{2}{3}}} = \frac{{3.97029191}}{{ - 0.40546511}} = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 9.79194469}}\] \[{\log _{\frac{2}{3}}}53 = \frac{{\log 53}}{{\log \frac{2}{3}}} = \frac{{1.72427587}}{{ - 0.17609126}} = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 9.79194469}}\]

Shunday qilib, boshida ta'kidlaganimizdek, qaysi logarifmdan foydalanishimiz muhim emas, oxirida biz bir xil javobni olamiz.