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.
-$$\log _ { 2 } ( x - 2 ) - \log _ { 2 } ( x - 3 ) = 4$$
A) $\left\{ \frac { 46 } { 15 } \right\}$
B) $\left\{ \frac { 1 } { 15 } \right\}$
C) $\left\{ - \frac { 46 } { 15 } \right\}$
D) $\varnothing$ )

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be rewritten as $\log_2\left(\frac{x-2}{x-3}\right) = 4$. Solving this equation for $x$ yields $x = \frac{46}{15}$. This value is in the domain of the original logarithmic expressions, as it makes both $x-2$ and $x-3$ positive.

Solve the Logarithmic Equation log⁡2(x−2)−log⁡2(x−3)=4\log _ { 2 } ( x - 2 ) - \log _ { 2 } ( x - 3 ) = 4log2​(x−2)−log2​(x−3)=4

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