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

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be simplified to $3x = 5(x - 2)$, solving this gives $x = 5$, which is in the domain of the original expression.

Solve the Logarithmic Equation log⁡3x=log⁡5+log⁡(x−2)\log 3 x = \log 5 + \log ( x - 2 )log3x=log5+log(x−2)

Solve the Logarithmic Equation $\log 3 x = \log 5 + \log ( x - 2 )$