Solve the equation and express the solution in exact form.
-$\log 2 x = \log 3 + \log ( x - 4 )$
A) $\{ 12 \}$
B) $\{ 4 \}$
C) $\left\{ - \frac { 12 } { 5 } \right\}$
D) $\{ - 1 \}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the right side of the equation: $\log 2x = \log 3 + \log (x - 4)$ becomes $\log 2x = \log [3(x - 4)]$. Since the logs are equal, their arguments must be equal: $2x = 3(x - 4)$. Solving this equation gives $x = 12$.

Solve the Equation and Express the Solution in Exact Form log⁡2x=log⁡3+log⁡(x−4)\log 2 x = \log 3 + \log ( x - 4 )log2x=log3+log(x−4)

Solve the Equation and Express the Solution in Exact Form $\log 2 x = \log 3 + \log ( x - 4 )$