Step 1 :The logarithmic equation \(\log _{6} x=5\) can be converted to exponential form by using the definition of a logarithm.
Step 2 :The base of the logarithm becomes the base of the power, the right side of the equation becomes the exponent, and the result is the number inside the logarithm.
Step 3 :So, the exponential form of the equation is \(6^5 = x\).
Step 4 :By calculating, we find that \(x = 7776.0\).
Step 5 :Final Answer: The logarithmic equation \(\log _{6} x=5\) in exponential form is \(6^5 = x\), which simplifies to \(x = \boxed{7776}\).