Step 1 :Understand that logarithms are the inverse operations to exponentiation.
Step 2 :Identify the base, exponent, and result for each equation.
Step 3 :For equation (a), the base is 3, the exponent is 4, and the result is 81.
Step 4 :For equation (b), the base is 10, the exponent is -4, and the result is 0.0001.
Step 5 :Rewrite each equation using the identified base, exponent, and result.
Step 6 :The logarithmic form of \(3^{4}=81\) is \(\log_{3}{81}=4\).
Step 7 :The exponential form of \(\log 0.0001=-4\) is \(10^{-4}=0.0001\).
Step 8 :\(\boxed{\log_{3}{81}=4}\) is the final answer for equation (a).
Step 9 :\(\boxed{10^{-4}=0.0001}\) is the final answer for equation (b).