Solve the equation.
-$\log x + \log ( x - 11 ) = \log ( x - 35 )$
A) $\{ - 7 , - 5 \}$
B) $\{ 7,5 \}$
C) $\{ 7 \}$
D){ }

Question

Solve the equation.
-$\log x + \log ( x - 11 ) = \log ( x - 35 )$
A) $\{ - 7 , - 5 \}$
B) $\{ 7,5 \}$
C) $\{ 7 \}$
D){  }

Quizplus · Accepted Answer

Using the properties of logarithms, we can combine the left side: $\log x + \log (x - 11) = \log (x(x - 11))$. The equation becomes $\log (x(x - 11)) = \log (x - 35)$. Since the logarithms are equal, the arguments must be equal: $x(x - 11) = x - 35$. Simplifying gives a quadratic equation: $x^2 - 11x = x - 35$, which simplifies to $x^2 - 12x + 35 = 0$. Factoring or using the quadratic formula gives $x = 7$ or $x = 5$. However, substituting these values back into the original equation, $x = 5$ does not work because it makes $\log(x - 11)$ undefined. Therefore, the only solution that works in the original equation is $x = 7$, but due to the format of the answer choices, the correct selection is D, indicating no solution from the provided options matches the correct answer.

Solve the Equation log⁡x+log⁡(x−11)=log⁡(x−35)\log x + \log ( x - 11 ) = \log ( x - 35 )logx+log(x−11)=log(x−35)

Solve the Equation $\log x + \log ( x - 11 ) = \log ( x - 35 )$