Definition of a logarithm:
if by = x, then logb x = y
Some useful properties of logarithms: (where a and b are unique bases of the logarithm)
logb(xy) = logb x + logb y
logb(x/y) = logb x - logb y
logbxp = p logb x
lim logb x = -∞, b > 1
x→0+
lim logb x = +∞, b > 1
x→+∞
lim logb x = logb (lim x)
x→c x→c
logb 1 = 0
logb b = 1
blogb x = x, x > 0
logb bx = x
logb x = loga x / loga b, b > 0, b ≠ 1
yx = bx logb y, b > 0, b ≠ 1