Solve the equation.
-$\log 3 x = \log 5 + \log ( x - 4 )$
A) $\frac { 1 } { 2 }$
B) $- 10$
C)$-\frac { 5 } { 2 }$
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 logarithms are equal, their arguments must be equal: $3x = 5(x - 4)$. Solving 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 )log3x=log5+log(x−4)

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