While it is right that errors are not represented evenly even on a logarithmic scale, it is still a useful approximation to make. In fact the integer value of

While it is right that errors are not represented evenly even on a logarithmic scale, it is still a useful approximation to make. In fact the integer value of the binary representation of a float approximates crudely the logarithm of the float. This was used in Quake's famous inverse square root approximation