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

The given expression can be expanded using the properties of logarithms as follows: $11 \ln \sqrt { a \left( b ^ { 2 } + c ^ { 2 } \right) }$ can be rewritten as $11 \ln \left( a \left( b ^ { 2 } + c ^ { 2 } \right) \right)^{1/2}$. Using the property $\ln x^{n} = n \ln x$, this becomes $11 \cdot \frac{1}{2} \ln \left( a \left( b ^ { 2 } + c ^ { 2 } \right) \right)$. Then, applying the property that $\ln xy = \ln x + \ln y$, it becomes $\frac{11}{2} \ln(a) + \frac{11}{2} \ln(b^2 + c^2)$, which matches choice B.

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