### Instruction: Evaluate $\log_{3}{81}-\log_{3}{\frac{1}{9}}$.### Response: I know that $\log_{3}{81}$ is the exponent I need to raise 3 to in order to get 81.
I also know that 3 to the fourth power is 81, so $\log_{3}{81}=4$.
Similarly, $\log_{3}{\frac{1}{9}}$ is the exponent I need to raise 3 to in order to get $\frac{1}{9}$.
I know that 3 to the negative second power is $\frac{1}{9}$, so $\log_{3}{\frac{1}{9}}=-2$.
Now I have $\log_{3}{81}-\log_{3}{\frac{1}{9}}=4-(-2)$.
I can simplify this by adding 2 to both sides, and I get $\log_{3}{81}-\log_{3}{\frac{1.}{9}}=4+2=6$.