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Power Rule
Reference
> Algebra: Natural Logarithms
Description
The Power Rule states that:
ln
(
x
y
)
=
y
ln
x
\ln{({x}^{y})}=y\ln{x}
ln
(
x
y
)
=
y
ln
x
Examples
4
ln
2
4\ln{2}
4
ln
2
1
Use
Power Rule
:
log
b
x
c
=
c
log
b
x
\log_{b}{{x}^{c}}=c\log_{b}{x}
lo
g
b
x
c
=
c
lo
g
b
x
.
ln
(
2
4
)
\ln{({2}^{4})}
ln
(
2
4
)
2
Simplify
2
4
{2}^{4}
2
4
to
16
16
1
6
.
ln
16
\ln{16}
ln
1
6
Done
Decimal Form: 2.772589
ln(16)
English
Power Rule