Solve the equation.
-$$\log _ { 3 } t + \log _ { 3 } ( t + 2 ) = \log _ { 3 } 80$$
A) $\{ 39 \}$
B) $\{ 10 \}$
C) $\{ 8 \}$
D) $\{ - 10,8 \}$

Question

Quizplus · Accepted Answer

Using the property of logarithms, $\log_b x + \log_b y = \log_b (xy)$, we can rewrite the equation as $\log_3 (t(t+2)) = \log_3 80$. This implies $t(t+2) = 80$. Solving the quadratic equation $t^2 + 2t - 80 = 0$ gives the solutions $t = 8$ and $t = -10$. However, since the logarithm of a negative number is undefined, the only valid solution is $t = 8$.

Solve the Equation log⁡3t+log⁡3(t+2)=log⁡380\log _ { 3 } t + \log _ { 3 } ( t + 2 ) = \log _ { 3 } 80log3​t+log3​(t+2)=log3​80

Solve the Equation $\log _ { 3 } t + \log _ { 3 } ( t + 2 ) = \log _ { 3 } 80$