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.
-$\log _ { 3 } ( x + 6 ) + \log _ { 3 } ( x - 6 ) - \log _ { 3 } x = 2$
A) $\{ 12 \}$
B) $\{ 12 , - 3 \}$
C) $\{ - 3 \}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the given equation can be simplified and solved to find x = 12. The other potential solution, x = -3, is not in the domain of the original logarithmic expressions because it would result in a negative argument for the logarithms.

Solve the Logarithmic Equation log⁡3(x+6)+log⁡3(x−6)−log⁡3x=2\log _ { 3 } ( x + 6 ) + \log _ { 3 } ( x - 6 ) - \log _ { 3 } x = 2log3​(x+6)+log3​(x−6)−log3​x=2

Solve the Logarithmic Equation $\log _ { 3 } ( x + 6 ) + \log _ { 3 } ( x - 6 ) - \log _ { 3 } x = 2$