Solve the equation. $\log ( x - 50 ) - \log 9 = \log ( x - 30 ) - \log x$
A) $\quad x = 5$
B) $x = 58$
C) $x = 54$
D) $x = 56$
E) none of these

Question

Quizplus · Accepted Answer

By using the properties of logarithms, the equation simplifies to $\log \frac{x-50}{9} = \log \frac{x-30}{x}$. Equating the arguments gives $\frac{x-50}{9} = \frac{x-30}{x}$. Solving this equation results in $x = 54$.

Solve the Equation log⁡(x−50)−log⁡9=log⁡(x−30)−log⁡x\log ( x - 50 ) - \log 9 = \log ( x - 30 ) - \log xlog(x−50)−log9=log(x−30)−logx

Solve the Equation $\log ( x - 50 ) - \log 9 = \log ( x - 30 ) - \log x$