Logarithm of b to base a is called the power which the a should be exponentiated to get the b:

c = log _{a }b
⇔
a^{c} = b
, and
b > 0, a > 0,
a ≠ 1

a
^{
log a b
}
= b

log _{a }1 = 0

log _{a }a = 1

log _{a }a^{n} = n

log _{a }(u ∙ v) =
log _{a }u
+
log _{a }v

log _{a }u ^{n}
=
n ∙ log _{a }u

log _{n }a
∙
log _{m }b
=
log _{m }a
∙
log _{n }b

a
^{
log n b
}
=
b
^{
log n a
}

Parametric derivative step by step sample

Fraction decomposition step by step sample