Berikut ialah sifat-sifat logaritma asli:

• ln ⁡ ( 1 ) = 0 {\displaystyle \ln(1)=0\,}

• ln ⁡ ( − 1 ) = i π {\displaystyle \ln(-1)=i\pi \quad \,} (lihat logaritma kompleks)

• ln ⁡ ( x ) < ln ⁡ ( y ) f o r 0 < x < y {\displaystyle \ln(x)<\ln(y)\quad {\rm {for}}\quad 0<x<y\;}

• h 1 + h ≤ ln ⁡ ( 1 + h ) ≤ h f o r h > − 1 {\displaystyle {\frac {h}{1+h}}\leq \ln(1+h)\leq h\quad {\rm {for}}\quad h>-1\;}

• lim x → 0 ln ⁡ ( 1 + x ) x = 1. {\displaystyle \lim _{x\to 0}{\frac {\ln(1+x)}{x}}=1.\,}