Solve the equation.
-$\log ( 3 x ) = \log 5 + \log ( x - 4 )$
A) $\left\{ - \frac { 5 } { 2 } \right\}$
B) $\left\{ \frac { 1 } { 2 } \right\}$
C) $\{ - 10 \}$
D) $\{ 10 \}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the right side of the equation: $\log(5) + \log(x - 4) = \log(5(x - 4))$. Thus, the equation becomes $\log(3x) = \log(5(x - 4))$. Since the logarithmic functions are equal, their arguments must be equal: $3x = 5(x - 4)$. Solving this equation for $x$, we get $3x = 5x - 20$, leading to $2x = 20$ and $x = 10$.

Solve the Equation log⁡(3x)=log⁡5+log⁡(x−4)\log ( 3 x ) = \log 5 + \log ( x - 4 )log(3x)=log5+log(x−4)

Solve the Equation $\log ( 3 x ) = \log 5 + \log ( x - 4 )$