Solve the equation.
-$\log (2+\mathrm{x})-\log (\mathrm{x}-5)=\log 2$
A) $\{-12\}$
B) $\{12\}$
C) $\varnothing$
D) $\left\{\frac{5}{2}\right\}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $\log (2+x) - \log (x-5) = \log \frac{2+x}{x-5}$. Setting this equal to $\log 2$, we have $\frac{2+x}{x-5} = 2$. Solving this equation gives $x = 12$. Checking the domain, $x$ must be greater than 5, so $x = 12$ is valid.

Solve the Equation log⁡(2+x)−log⁡(x−5)=log⁡2\log (2+\mathrm{x})-\log (\mathrm{x}-5)=\log 2log(2+x)−log(x−5)=log2 A) {−12}\{-12\}{−12} B) {12}\{12\}{12} C) ∅\varnothing∅ D) {52}\left\{\frac{5}{2}\right\}{25​}

Solve the Equation $\log (2+\mathrm{x})-\log (\mathrm{x}-5)=\log 2$ A) $\{-12\}$ B) $\{12\}$ C) $\varnothing$ D) $\left\{\frac{5}{2}\right\}$