To write the equation \( \sqrt[4]{16} = 2 \) in its equivalent logarithmic form, we start with the general relationship between exponents and logarithms.
The expression \( \sqrt[4]{16} \) can be written as \( 16^{1/4} \), and we denote the equation as follows:
If \( b^y = x \), then the logarithmic form is \( \log_b(x) = y \).
In this case:
- \( b = 4 \) (the index of the root)
- \( x = 16 \) (the number under the root)
- \( y = 2 \) (the result)
Thus, we can write it in logarithmic form as:
\[ \log_4{16} = 2 \]
So, the equation in logarithmic form is:
\[ \log_4{16} = 2 \]