Logarithm of
b
to base
a
is called the power which the
a
should be exponentiated to get the
b:
c = log a b
⇔
ac = b
, and
b > 0, a > 0,
a ≠ 1
Basic features of the logarithms:
a
log a b
= b
log a 1 = 0
Logarithm of the product:
log a (u ∙ v) =
log a u
+
log a v
Logarithm of the division:
Logarithm of the powers and roots:
Transfer to the new logarithm base formula:
Formulas, derived from logarithm features:
log n a
∙
log m b
=
log m a
∙
log n b
a
log n b
=
b
log n a
Logarithms comparison: