Solve the equation. $$\log ( x - 28 ) - \log 8 = \log ( x - 16 ) - \log x$$
A) $\quad x = 32$
B) $x = 34$
C) $x = 4$
D) $x = 36$
E) none of these

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the logs on each side: $\log\left(\frac{x-28}{8}\right) = \log\left(\frac{x-16}{x}\right)$. Since the logs are equal, the arguments must be equal: $\frac{x-28}{8} = \frac{x-16}{x}$. Solving this equation for $x$ gives $x = 32$.

Solve the Equation log⁡(x−28)−log⁡8=log⁡(x−16)−log⁡x\log ( x - 28 ) - \log 8 = \log ( x - 16 ) - \log xlog(x−28)−log8=log(x−16)−logx

Solve the Equation $\log ( x - 28 ) - \log 8 = \log ( x - 16 ) - \log x$