Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm
whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$\log x + \log \left( x ^ { 2 } - 4 \right) - \log 3 - \log ( x - 2 )$
A) $\log \frac { x ( x + 2 ) } { 3 }$
B) $\log \frac { x ( x - 4 ) } { 3 ( x - 2 ) }$
C) $\log \frac { x ( x - 4 ) ( x - 2 ) } { 3 }$
D) $\log \frac { 2 x + 2 ) } { 5 - x }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the given expression can be simplified as follows: $\log x + \log(x^2 - 4) - \log 3 - \log(x - 2)$ can be rewritten using the property $\log a + \log b = \log(ab)$ and $\log a - \log b = \log(\frac{a}{b})$, resulting in $\log \frac{x(x^2 - 4)}{3(x - 2)}$. Factoring $x^2 - 4$ as $(x + 2)(x - 2)$ and simplifying gives $\log \frac{x(x + 2)}{3}$.

Use Properties of Logarithms to Condense the Logarithmic Expression log⁡x+log⁡(x2−4)−log⁡3−log⁡(x−2)\log x + \log \left( x ^ { 2 } - 4 \right) - \log 3 - \log ( x - 2 )logx+log(x2−4)−log3−log(x−2)

Use Properties of Logarithms to Condense the Logarithmic Expression $\log x + \log \left( x ^ { 2 } - 4 \right) - \log 3 - \log ( x - 2 )$