# log5*5^4

Logarithms
$$\displaystyle{\log{{5}}}\cdot{5}^{{4}}$$

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, $$\displaystyle{\log{{5}}}\cdot{5}^{{4}}={4}$$