Tính chất Logarit_tự_nhiên

  • ln ⁡ ( 1 ) = 0 {\displaystyle \ln(1)=0\,}
  • ln ⁡ ( − 1 ) = i π {\displaystyle \ln(-1)=i\pi \quad \,}
  • ln ⁡ ( x ) < ln ⁡ ( y ) , 0 < x < y {\displaystyle \ln(x)<\ln(y)\quad {\rm {,}}\quad 0<x<y\;}
  • h 1 + h ≤ ln ⁡ ( 1 + h ) ≤ h , h > − 1 {\displaystyle {\frac {h}{1+h}}\leq \ln(1+h)\leq h\quad {\rm {,}}\quad h>-1\;}
  • lim x → 0 ln ⁡ ( 1 + x ) x = 1 {\displaystyle \lim _{x\to 0}{\frac {\ln(1+x)}{x}}=1\,}