As an employer, you want to save time, be more productive, and increase the cohesion among your team. Finding the right way to do this is always the challenge. Fortunately, there are tools out there that are cost effective that enable employees to be more productive and work together as a team.
There is both top down quantifiable data and bottom up anecdotal stories available to justify the [small] budget needed for a knowledge base.
Stack both the hard data with the soft data and get the buy in from parties interested in quantifiable business measurements and those who appreciate the less quantifiable benefits. Everyone ends up happy and warm in the belly.