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Definition of Natural Logarithm
Reference
> Algebra: Natural Logarithms
Description
The Definition of Natural Logarithm Rule states that:
e
y
=
x
{e}^{y}=x
e
y
=
x
if and only if
ln
x
=
y
\ln{x}=y
ln
x
=
y
Examples
e
4
x
=
3
{e}^{4x}=3
e
4
x
=
3
1
Use
Definition of Natural Logarithm
:
e
y
=
x
{e}^{y}=x
e
y
=
x
if and only if
ln
x
=
y
\ln{x}=y
ln
x
=
y
.
4
x
=
ln
3
4x=\ln{3}
4
x
=
ln
3
2
Divide both sides by
4
4
4
.
x
=
ln
3
4
x=\frac{\ln{3}}{4}
x
=
4
ln
3
Done
Decimal Form: 0.274653
x=ln(3)/4
English
Definition of Natural Logarithm