How do I find the value of ##log 100##?

First, you must rewrite this in exponential form.

log is the inverse of exponential. You must rewrite it in that form to figure it out without a calculator. First, figure out your base, the subscript to log. In this case, it is not specified, so the general base is ten. The x value you were trying to find is now the exponent to your base and in this case ##10^x=100## . You know through common sense that ##10^2## =100 so x=2. Therefore, the ##log100## = 2