Solve the logarithmic equation for x. Give an exact solution
-$\log _ { 3 } ( x + 2 ) - \log _ { 3 } ( x - 4 ) = 3$
A) $\frac { 3 } { 13 }$
B) $\frac { 19 } { 4 }$
C) 21
D) $\frac { 55 } { 13 }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can simplify the equation as follows:$\log _ { 3 } ( x + 2 ) - \log _ { 3 } ( x - 4 ) = 3$$\log _ { 3 } \left ( \frac { x + 2 } { x - 4 } \right ) = 3$$\frac { x + 2 } { x - 4 } = 3 ^ { 3 } = 27$$x + 2 = 27 ( x - 4 )$$x + 2 = 27 x - 108$$-26 x = -110$$x = \frac { 110 } { 26 } = \frac { 55 } { 13 }$

Solve the Logarithmic Equation for X log⁡3(x+2)−log⁡3(x−4)=3\log _ { 3 } ( x + 2 ) - \log _ { 3 } ( x - 4 ) = 3log3​(x+2)−log3​(x−4)=3

Solve the Logarithmic Equation for X $\log _ { 3 } ( x + 2 ) - \log _ { 3 } ( x - 4 ) = 3$