Reglas para x,y>0x,y>0
log⁡a(xy)=log⁡ax+log⁡ay\log_a(xy)=\log_a x+\log_a y, log⁡axy=log⁡ax−log⁡ay\log_a\dfrac{x}{y}=\log_a x-\log_a y, log⁡a(xm)=mlog⁡ax\log_a(x^m)=m\log_a x para x>0x>0. Todas las identidades se derivan de la definición y leyes de los poderes; en ecuaciones, cada logaritmo debe tener un argumento positivo en el paso en el que se aplica una fórmula.
log⁡a1=0\log_a 1=0, log⁡aa=1\log_a a=1
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