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Mathematics
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Logarithms
Logarithms
5 formulas · Mathematics
Definition of a logarithm
log
a
b
=
c
⟺
a
c
=
b
\log_a b=c \iff a^c=b
lo
g
a
b
=
c
⟺
a
c
=
b
Logarithm of a product
log
a
(
x
y
)
=
log
a
x
+
log
a
y
\log_a(xy)=\log_a x+\log_a y
lo
g
a
(
x
y
)
=
lo
g
a
x
+
lo
g
a
y
Logarithm of a quotient
log
a
x
y
=
log
a
x
−
log
a
y
\log_a\tfrac{x}{y}=\log_a x-\log_a y
lo
g
a
y
x
=
lo
g
a
x
−
lo
g
a
y
Logarithm of a power
log
a
x
k
=
k
log
a
x
\log_a x^k=k\log_a x
lo
g
a
x
k
=
k
lo
g
a
x
Change of base of a logarithm
log
a
b
=
log
c
b
log
c
a
\log_a b=\dfrac{\log_c b}{\log_c a}
lo
g
a
b
=
lo
g
c
a
lo
g
c
b
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