Solve the logarithmic equation. Give an exact solution.
-$$\log _ { 3 } ( x + 6 ) - \log _ { 3 } ( x - 3 ) = 3$$
A) $\left\{ \frac { 87 } { 26 } \right\}$
B) $\{ 18 \}$
C) $\left\{ \frac { 33 } { 8 } \right\}$
D) $\left\{ \frac { 9 } { 26 } \right\}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be rewritten as $\log_3\left(\frac{x+6}{x-3}\right) = 3$. Solving for $x$ gives $x = \frac{87}{26}$.

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

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