Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$\log ( 3 + x ) - \log ( x - 3 ) = \log 3$
A) $\{ 6 \}$
B) $\left\{ \frac { 3 } { 2 } \right\}$
C) $\{ - 6 \}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the left side into a single logarithm: $\log\left(\frac{3+x}{x-3}\right) = \log(3)$. Solving the equation $\frac{3+x}{x-3} = 3$ gives $x = 6$, which is in the domain of the original logarithmic expressions.

Solve the Logarithmic Equation log⁡(3+x)−log⁡(x−3)=log⁡3\log ( 3 + x ) - \log ( x - 3 ) = \log 3log(3+x)−log(x−3)=log3

Solve the Logarithmic Equation $\log ( 3 + x ) - \log ( x - 3 ) = \log 3$