This is essentially the way many 8 bit games did 3d rendering ( for example the world famous Elite )... you just need two tables, one linear2log and another log2linear, with careful measurement of the ranges and number of elements needed in you application ( which is easy for inference ).
ps. Also used in the original circuits of the Yamaha DX7 synthetiser ( https://www.righto.com/2021/11/reverse-engineering-yamaha-dx... ).