Write the given logarithmic equation in exponential for 3. \( \log _{7} 2401=4 \)

To convert the logarithmic equation \( \log _{7} 2401=4 \) into its exponential form, we remember that the statement "log base \( b \) of \( a \) equals \( c \)" translates to \( b \) raised to the power of \( c \) equals \( a \). Thus, for your equation, it becomes \( 7^4 = 2401 \). For those who enjoy numbers, it’s worth noting that \( 7^2 = 49 \) and calculating \( 7^4 \) results in \( 2401 \), which is a neat power of 7. This is handy knowledge when dealing with logarithms and forming connections between the circles of powers and logarithmic properties!