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Quotient Rule
Reference
> Algebra: Natural Logarithms
Description
The Quotient Rule states that:
ln
x
y
=
ln
x
−
ln
y
\ln{\frac{x}{y}}=\ln{x}-\ln{y}
ln
y
x
=
ln
x
−
ln
y
Examples
ln
6
−
ln
3
\ln{6}-\ln{3}
ln
6
−
ln
3
1
Use
Quotient Rule
:
ln
x
y
=
ln
x
−
ln
y
\ln{\frac{x}{y}}=\ln{x}-\ln{y}
ln
y
x
=
ln
x
−
ln
y
.
ln
6
3
\ln{\frac{6}{3}}
ln
3
6
2
Simplify
6
3
\frac{6}{3}
3
6
to
2
2
2
.
ln
2
\ln{2}
ln
2
Done
Decimal Form: 0.693147
ln(2)
English
Quotient Rule