LOGARITHMS
Definition
log_a(x)=b iff a^b=x
Properties
log_a(1)=0
log_a(a)=1
log_a(a^n)=n
log_a(x^p)=p·log_a(x)
log_a(x1·x2)=log_a(x1)+log_a(x2)
log_a(x1/x2)=log_a(x1)-log_a(x2)
Domain Conditions
a>0, a≠1, x>0
Change of Base
log_b(x)=log_a(x)/log_a(b)=ln(x)/ln(b)=log(x)/log(b)
Definition
log_a(x)=b iff a^b=x
Properties
log_a(1)=0
log_a(a)=1
log_a(a^n)=n
log_a(x^p)=p·log_a(x)
log_a(x1·x2)=log_a(x1)+log_a(x2)
log_a(x1/x2)=log_a(x1)-log_a(x2)
Domain Conditions
a>0, a≠1, x>0
Change of Base
log_b(x)=log_a(x)/log_a(b)=ln(x)/ln(b)=log(x)/log(b)
