Solve the equation.
-$\log ( 5 + x ) - \log ( x - 4 ) = \log 4$
A) $\{ - 7 \}$
B) $\left\{ \frac { 3 } { 2 } \right\}$
C) $\{ 7 \}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the left side into a single logarithm: $\log\left(\frac{5+x}{x-4}\right) = \log(4)$. Since the logarithms are equal, the arguments must be equal: $\frac{5+x}{x-4} = 4$. Solving this equation for $x$ gives $x = 7$, which is a valid solution because it makes both the original logarithmic expressions defined (i.e., both $5 + x > 0$ and $x - 4 > 0$ when $x = 7$).

Solve the Equation log⁡(5+x)−log⁡(x−4)=log⁡4\log ( 5 + x ) - \log ( x - 4 ) = \log 4log(5+x)−log(x−4)=log4

Solve the Equation $\log ( 5 + x ) - \log ( x - 4 ) = \log 4$