Write the equation in its equivalent logarithmic form. \[ 6^{4}=1296 \] What is the equivalent logarithmic form of the equation?

Step 1 ：The given equation is in exponential form: \(6^{4}=1296\).

Step 2 ：To convert it to logarithmic form, we need to understand the relationship between exponential and logarithmic forms. The exponential form is \(b^y = x\), where b is the base, y is the exponent, and x is the result. The equivalent logarithmic form is \(\log_b(x) = y\), where \(\log_b(x)\) is the logarithm of x to the base b, and y is the result.

Step 3 ：In the given equation, 6 is the base, 4 is the exponent, and 1296 is the result.

Step 4 ：So, the equivalent logarithmic form would be \(\log_6(1296) = 4\).

Step 5 ：Final Answer: The equivalent logarithmic form of the equation \(6^{4}=1296\) is \(\boxed{\log_{6}{1296} = 4}\).