Common Logarithm of e

log₁₀ e = 0.4342944819 is the reciprocal of ln 10 and converts the other way: log₁₀ x = 0.434294 × ln x. Nineteenth-century texts called it the modulus of the common system of logarithms and printed it on the flyleaf of every table, because with logarithms done by lookup the conversion factor was needed constantly and a slip in it corrupted a whole calculation.

It is also the derivative that makes base-10 calculus awkward: d(log₁₀ x)/dx = 0.434294/x rather than the clean 1/x of the natural logarithm, which is exactly why analysis abandoned base 10 while measurement kept it. The number survives today mostly inside library implementations — the constant M_LOG10E in the C standard library and Math.LOG10E in JavaScript — quietly converting between the log the hardware computes and the log the user asked for.