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.
-$\log ( x + 5 ) = \log ( 4 x - 4 )$
A) $\{ 3 \}$
B) $\left\{ \frac { 3 } { 2 } \right\}$
C) $\{ - 3 \}$
D) $\left\{ \frac { 1 } { 3 } \right\}$

Question

Quizplus · Accepted Answer

For the equation $\log(x + 5) = \log(4x - 4)$, since the logarithms are equal, their arguments must be equal. Thus, $x + 5 = 4x - 4$. Solving for $x$, we subtract $x$ from both sides and add $4$ to both sides to get $5 + 4 = 4x - x$, which simplifies to $9 = 3x$. Dividing both sides by $3$, we find $x = 3$. This value is in the domain of the original logarithmic expressions, as both $x + 5$ and $4x - 4$ are positive when $x = 3$.

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

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