Solve the equation.
-$$\log _ { 3 } r + \log _ { 3 } ( r - 8 ) = 2$$
A) $\{ 9 \}$
B) $\{ 8.5 \}$
C) $\varnothing$
D) $\{ 1 \}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be combined as $\log_3(r(r - 8)) = 2$. Converting to exponential form gives $3^2 = r(r - 8)$, leading to $r^2 - 8r - 9 = 0$. Factoring or using the quadratic formula yields $r = 9$ or $r = -1$. Since $r - 8$ must be positive for the logarithm to be defined, the only solution is $r = 9$.

Solve the Equation log⁡3r+log⁡3(r−8)=2\log _ { 3 } r + \log _ { 3 } ( r - 8 ) = 2log3​r+log3​(r−8)=2

Solve the Equation $\log _ { 3 } r + \log _ { 3 } ( r - 8 ) = 2$