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.
-$2 \log x - \log 6 = \log 96$
A) $\{ 24 \}$
B) $\{ - 24 \}$
C) $\{ 24 , - 24 \}$
D) $\{ 288 \}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be simplified to $\log(x^2) - \log(6) = \log(96)$, which simplifies further to $\log(\frac{x^2}{6}) = \log(96)$. Solving for $x^2$ gives $x^2 = 576$, so $x = 24$. Negative values are not in the domain of the logarithmic function, so $x = -24$ is rejected.

Solve the Logarithmic Equation 2log⁡x−log⁡6=log⁡962 \log x - \log 6 = \log 962logx−log6=log96

Solve the Logarithmic Equation $2 \log x - \log 6 = \log 96$