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

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

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be rewritten as $\log \frac{2+x}{x-5} = \log 2$. By equating the arguments, $\frac{2+x}{x-5} = 2$. Solving this gives $x = 12$.

Solve the Equation log⁡(2+x)−log⁡(x−5)=log⁡2\log ( 2 + x ) - \log ( x - 5 ) = \log 2log(2+x)−log(x−5)=log2

Solve the Equation $\log ( 2 + x ) - \log ( x - 5 ) = \log 2$