Step 1 :Express the given equation in exponential form. The given equation is \(6 \log _{46656} 6=1\)
Step 2 :The logarithm base b of a number x is equal to y if and only if b raised to the power of y is equal to x. In other words, if \(\log_b(x) = y\), then \(b^y = x\).
Step 3 :In the given equation, the base of the logarithm is 46656, the number inside the logarithm is 6, and the result of the logarithm operation is 1/6.
Step 4 :Therefore, the equivalent equation in exponential form should be 46656 raised to the power of 1/6 equals 6.
Step 5 :\(\boxed{46656^{\frac{1}{6}} = 6}\)