section_path: Analytic properties/Transcendence of the logarithm
section_name: Transcendence of the logarithm
paragraph_text: Transcendence of the logarithm
  
  Real numbers that are not algebraic are called transcendental; for example, π and e are such numbers, but 2 − 3 {\displaystyle {\sqrt {2-{\sqrt {3}}}}} is not. Almost all real numbers are transcendental. The logarithm is an example of a transcendental function. The Gelfond–Schneider theorem asserts that logarithms usually take transcendental, i.e. "difficult" values.