log122

log122 is a shorthand sometimes used to denote the logarithm of 2 with base 12, written as log base 12 of 2 (log_12(2)). In this form, it answers the question: to what exponent must 12 be raised to obtain 2?

If y = log_12(2), then by definition 12^y = 2. This value is positive and lies between 0 and 1 because the base 12 is greater than 1 and 2 is between 1 and 12.

The logarithm can be computed using the change-of-base formula: log_12(2) = ln(2) / ln(12). Numerically, ln(2) ≈ 0.6931 and ln(12) ≈ 2.4849, giving log_12(2) ≈ 0.279. Thus, 12^0.279 ≈ 2.

Properties include that the function is increasing for bases greater than 1, and log_12(2) is a non-integer positive number less than 1. It is irrational, since 2 is not an integer power of 12; equivalently, if log_12(2) were rational, it would imply a contradiction in the equality 2^q = 12^p for integers p, q.

Log_12(2) relates to other logarithms via log_12(2) = 1 / log_2(12) and log_12(2) = ln(2) / ln(12). While not as common in everyday calculations, it appears in contexts involving base-12 scaling or conversions between different logarithmic bases.