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Definition of Common Logarithm
Reference
> Algebra: Common Logarithms
Description
The Definition of Common Logarithm Rule states that:
b
a
=
x
{b}^{a}=x
b
a
=
x
if and only if
l
o
g
b
(
x
)
=
a
log_b(x)=a
l
o
g
b
(
x
)
=
a
Examples
3
y
=
7
{3}^{y}=7
3
y
=
7
1
Use
Definition of Common Logarithm
:
b
a
=
x
{b}^{a}=x
b
a
=
x
if and only if
l
o
g
b
(
x
)
=
a
log_b(x)=a
l
o
g
b
(
x
)
=
a
.
y
=
log
3
7
y=\log_{3}{7}
y
=
lo
g
3
7
2
Use
Change of Base Rule
:
log
b
x
=
log
a
x
log
a
b
\log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}
lo
g
b
x
=
l
o
g
a
b
l
o
g
a
x
.
y
=
log
7
log
3
y=\frac{\log{7}}{\log{3}}
y
=
lo
g
3
lo
g
7
Done
Decimal Form: 1.771244
y=log(7)/log(3)
English
Definition of Common Logarithm