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Power Rule
Reference
> Algebra: Common Logarithms
Description
The Power Rule states that:
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
Examples
4
log
3
2
4\log_{3}{2}
4
lo
g
3
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
.
log
3
2
4
\log_{3}{{2}^{4}}
lo
g
3
2
4
2
Simplify
2
4
{2}^{4}
2
4
to
16
16
1
6
.
log
3
16
\log_{3}{16}
lo
g
3
1
6
Done
Decimal Form: 2.523719
log(3,16)
English
Power Rule