What is the meaning of a logarithm of a unit?
Logarithms of quantities with units occur meaningfully. For example, the electrostatic potential near a long, charged cylinder is proportional to the logarithm of the distance from the cylinder. However, the value that one calculates from such a formula depends on the units of length that one uses. A meaningful physical quantity based on a potential is always the difference between potentials at two points. Such a calculation will include a term of the form log (r2) – log (r1), (1) which is equal to log (r2 / r1). (2) Therefore, in the final analysis, the units of length cancel out. This cancellation is not good enough for The Universal Units Calculator. Logarithms of quantities with units can occur as intermediate quantities in calculations similar to expression (1). The aim of The Universal Units Calculator is to keep proper track of units throughout any meaningful calculation. In keeping with this aim, The Universal Units Calculator keeps track of logarithms of units. The basic prin
