We are given: \(\displaystyle{\log{{5}}}\cdot{5}^{{4}}\)

Let \(y=\log5\cdot5^{4}\ \text{and write in exponential for m}:\log bx=a\to b^{a}=x\)

\(\displaystyle{5}^{{y}}={5}^{{4}}\)

Equating exponents, we have: \(y=4\)

Hence, \(\displaystyle{\log{{5}}}\cdot{5}^{{4}}={4}\)