Use the properties of logarithms to expand the quantity.
$11 \ln \sqrt { a \left( b ^ { 2 } + c ^ { 2 } \right) }$
A) $\frac { \ln ( a ) } { 11 } + \frac { \ln ( 2 b + 2 c ) } { 11 }$
B)
$\frac { 11 \ln ( a ) } { 2 } + \frac { 11 \ln \left( b ^ { 2 } + c ^ { 2 } \right) } { 2 }$
C) $11 \ln ( a ) - 11 \ln \left( b ^ { 2 } + c ^ { 2 } \right)$
D)
$\frac { \ln ( a ) } { 11 } - \frac { \ln \left( b ^ { 2 } + c ^ { 2 } \right) } { 11 }$
E) $11 \ln ( a ) + 11 \ln \left( b ^ { 2 } + c ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

We use the properties of logarithms:

$$ \ln (xy) = \ln x + \ln y $$
$$ \ln \left( \frac { x } { y } \right) = \ln x - \ln y $$
$$ \ln x ^ { n } = n \ln x $$
$$ \ln \sqrt x = \frac { 1 } { 2 } \ln x $$

$$ 11 \ln \sqrt { a \left( b ^ { 2 } + c ^ { 2 } \right) } = 11 \ln \left( a \cdot \sqrt { b ^ { 2 } + c ^ { 2 } } \right) $$
$$ = 11 \ln \left( a \right) + 11 \ln \left( \sqrt { b ^ { 2 } + c ^ { 2 } } \right) = \frac { 11 \ln \left( a \right) } { 2 } + \frac { 11 \ln \left( b ^ { 2 } + c ^ { 2 } \right) } { 2 } $$

Use the Properties of Logarithms to Expand the Quantity 11ln⁡a(b2+c2)11 \ln \sqrt { a \left( b ^ { 2 } + c ^ { 2 } \right) }11lna(b2+c2)​

Use the Properties of Logarithms to Expand the Quantity $11 \ln \sqrt { a \left( b ^ { 2 } + c ^ { 2 } \right) }$