Write the expression as a single logarithm. Assume all variables represent positive real numbers. $$\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 2 a \right) - \log ( a + 2 ) \right]$$
A) $\log \sqrt [ 3 ] { a }$
B) $\log \sqrt [ 3 ] { a ^ { 2 } + a - 2 }$
C) $\log _ { 1 / 3 } \left( a ^ { 2 } + a - 2 \right)$
D) $\log \left( a ^ { 3 } + 4 a ^ { 2 } + 4 a \right) ^ { 1 / 3 }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we have:$\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 2 a \right) - \log ( a + 2 ) \right]$$\frac { 1 } { 3 } \log \frac { a ^ { 2 } + 2 a } { a + 2 }$$\log \left( \frac { a ^ { 2 } + 2 a } { a + 2 } \right) ^ { 1 / 3 }$$\log \sqrt [ 3 ] { \frac { a ^ { 2 } + 2 a } { a + 2 } }$$\log \sqrt [ 3 ] { a ^ { 2 } + 2 a - 2 }$

Write the Expression as a Single Logarithm 13[log⁡(a2+2a)−log⁡(a+2)]\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 2 a \right) - \log ( a + 2 ) \right]31​[log(a2+2a)−log(a+2)]

Write the Expression as a Single Logarithm $\frac { 1 } { 3 } \left[ \log \left( a ^ { 2 } + 2 a \right) - \log ( a + 2 ) \right]$