The logarithm of a fraction is the difference of the logarithms of the numerator and the denominator. So, we can write log\(_{10}\)\(\frac{1}{40}\) as log\(_{10}\)(1) - log\(_{10}\)(40).

We know that log\(_{10}\)(1) = 0 and log\(_{10}\)(40) can be written as log\(_{10}\)(4) + log\(_{10}\)(10), which equals 0.6021 + 1 = 1.6021.

Therefore, log\(_{10}\)\(\frac{1}{40}\) = 0 - 1.6021 = -1.6021.