Solve the equation.
-$$\log _ { 5 } y + \log _ { 5 } ( 12 - y ) = \log _ { 5 } 35$$
A) $\{ - 23,35 \}$
B) $\{ 5,7 \}$
C) { }
D) $\{ - 7 , - 5 \}$

Question

Solve the equation.
-$$\log _ { 5 } y + \log _ { 5 } ( 12 - y ) = \log _ { 5 } 35$$
A) $\{ - 23,35 \}$
B) $\{ 5,7 \}$
C) {  }
D) $\{ - 7 , - 5 \}$

Quizplus · Accepted Answer

Using the property of logarithms that $\log_a b + \log_a c = \log_a (bc)$, we can combine the left side of the equation to get $\log_5(y(12-y)) = \log_5(35)$. This implies $y(12-y) = 35$, which simplifies to a quadratic equation $y^2 - 12y + 35 = 0$. Factoring or using the quadratic formula gives the solutions $y = 5$ and $y = 7$.

Solve the Equation log⁡5y+log⁡5(12−y)=log⁡535\log _ { 5 } y + \log _ { 5 } ( 12 - y ) = \log _ { 5 } 35log5​y+log5​(12−y)=log5​35

Solve the Equation $\log _ { 5 } y + \log _ { 5 } ( 12 - y ) = \log _ { 5 } 35$