MathDB

Let

A = \log (1) + \log 2 + \log(3) + \cdots + \log(2023)

and

B = \log(1/1) + \log(1/2) + \log(1/3) + \cdots + \log(1/2023).

What is the value of

A + B\ ?

(

logs are logs base

10)

\mathrm a. ~ 0\qquad \mathrm b.~1\qquad \mathrm c. ~{-\log(2023!)} \qquad \mathrm d. ~\log(2023!) \qquad \mathrm e. ~{-2023}

Problem Statement