Logarithmic Rules
Logarithm
Definition:
logb a = m  bm = a
Common Logarithm:
log10 = log
Natural Logarithm:
loge = ln
Change of Base:
logb a =
log5 13 =
Product Rule:
logb (xy) = logb x + logb y
log3 (4x) = log3 4 + log3 x
Quotient Rule:
logb
Power Rule:
p logb M = logb Mp
4 log5 x = log5 x4
Same Base
logb bx = x
log3 32 = 2
bbogb x
7log72 = 2
logb x = logb y  x = y
If log3 4 = log3 y
Then 4 = y
Logarithmic Equality
= logb M – logb N
log4 16 = 2
log5
42 = 16
= log5 x – log5 y