Solve the equation.
-$\log _{9}(x-8)+\log 9(x-8)=1$
A) $-\sqrt{65}, \sqrt{65}$
B) 11
C) $\sqrt{65}$
D) - 11,11

Name: Solve the equation. -$\log _{9}(x-8)+\log 9(x-8)=1$ A) $-\sqrt{65}, \sqrt{65}$ B) 11 C) $\sqrt{65}$ D) - 11,11
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Question

Quizplus · Accepted Answer

The equation simplifies to $\log_{9}((x-8)^2) = 1$, which implies $(x-8)^2 = 9$. Solving gives $x-8 = 3$ or $x-8 = -3$, leading to $x = 11$ or $x = 5$. However, $x = 5$ is not valid as it makes the argument of the logarithm negative. Thus, the solution is $x = 11$.

Solve the Equation log⁡9(x−8)+log⁡9(x−8)=1\log _{9}(x-8)+\log 9(x-8)=1log9​(x−8)+log9(x−8)=1 A) −65,65-\sqrt{65}, \sqrt{65}−65​,65​ B) 11 C) 65\sqrt{65}65​

Solve the Equation $\log _{9}(x-8)+\log 9(x-8)=1$ A) $-\sqrt{65}, \sqrt{65}$ B) 11
C) $\sqrt{65}$