Rewrite each of the following equations: (Make sure to preview each answer)
(a) Rewrite $3^{4}=81$ as a logarithmic equation:
(b) Rewrite $\log 0.0001=-4$ as an exponential equation:

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).