Solve the equation.
-$\log ( 5 + x ) - \log ( x - 3 ) = \log 3$
A) $\frac { 1 } { 2 }$
B) $- 7$
C) $\varnothing$
D) 7

Name: Solve the equation. -$\log ( 5 + x ) - \log ( x - 3 ) = \log 3$ A) $\frac { 1 } { 2 }$ B) $- 7$ C) $\varnothing$ D) 7
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Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the left side into a single logarithm: $\log\left(\frac{5+x}{x-3}\right) = \log(3)$. Since the logarithms are equal, the arguments must be equal: $\frac{5+x}{x-3} = 3$. Solving this equation for $x$ gives $x = 7$.

Solve the Equation log⁡(5+x)−log⁡(x−3)=log⁡3\log ( 5 + x ) - \log ( x - 3 ) = \log 3log(5+x)−log(x−3)=log3

Solve the Equation $\log ( 5 + x ) - \log ( x - 3 ) = \log 3$