Solve the logarithmic equation.
-$$\log _ { 9 } t ^ { 3 } = \log _ { 9 } t ^ { 2 } - 2$$
A) { }
B) $\left\{ \frac { 1 } { 81 } \right\}$
C) $\{ \sqrt [ 3 ] { 2 } \}$
D) $\{ 81 \}$

Question

Solve the logarithmic equation.
-$$\log _ { 9 } t ^ { 3 } = \log _ { 9 } t ^ { 2 } - 2$$
A) {  }
B) $\left\{ \frac { 1 } { 81 } \right\}$
C) $\{ \sqrt [ 3 ] { 2 } \}$
D) $\{ 81 \}$

Quizplus · Accepted Answer

Given the equation $\log_9 t^3 = \log_9 t^2 - 2$, we can use the property of logarithms that states if $\log_b x = \log_b y$, then $x = y$. Therefore, $t^3 = t^2 \cdot 9^{-2}$ because $9^{-2}$ is the exponential form of $-2$ in the base $9$. Simplifying, we get $t^3 = \frac{t^2}{81}$, which implies $t = \frac{1}{81}$ after dividing both sides by $t^2$ and assuming $t \neq 0$.

Solve the Logarithmic Equation log⁡9t3=log⁡9t2−2\log _ { 9 } t ^ { 3 } = \log _ { 9 } t ^ { 2 } - 2log9​t3=log9​t2−2

Solve the Logarithmic Equation $\log _ { 9 } t ^ { 3 } = \log _ { 9 } t ^ { 2 } - 2$