Tabiiy logarifm uchun asos ekanligini eslatib o'tamiz e va logarifmni eksponensial shaklga o'tkazish,

\[\ln {{\bf{e}}^4} = {\log _{\bf{e}}}{{\bf{e}}^4} = ?\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}{{\bf{e}}^?} = {{\bf{e}}^4}\]

Bundan biz tezda \({{\bf{e}}^4} = {{\bf{e}}^4}\) ekanligini ko'rishimiz mumkin va shuning uchun bizda shunday bo'lishi kerak,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{\ln {{\bf{e}}^4} = 4}}\]

E'tibor bering, bu logarifmning qiymatini aniqlashning osonroq usuli logarifmning xususiyatlarini esga olish edi. Xususan, ko'rsatilgan mulk,

\[{\log _b}{b^x} = x\]

Bundan foydalanib, biz logarifmning qiymatini juda tez ko'rishimiz mumkin.