Why do we need logs to solve exponential equations?

Can someone me i’m confused. will give brainliest and a whole bunch of points

Apinhole camera is made out of a light-tight box with a piece of film attached to one side and pinhole on the opposite side. the optimum diameter d(in millimeters) of the pinhole can be modeled by d=1.9[ (5.5 x 10^-4) l) ] ^1/2, where l is the length of the camera box (in millimeters). what is the optimum diameter for a pinhole camera if the camera box has a length of 10 centimeters

Iknow its nothing to do with education, but what type of thing should i wrote here? ? : ) its for mcdonald's btw.