Exponents and Logarithms

We remember that we had trouble at the very beginning with the function 2X (or 3X, or 10X). It was intuitively very plausible that there should be such functions, satisfying the fundamental equation 2x+y=2x2y for all numbers x, y, and 2° = 1, but we had difficulties in saying what we meant by % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaGaeGOmaiZaaWbaaSqabeaadaGcaaqaaiabikda % Yaadbeaaaaaaaa!3E04!$$ 2^{\sqrt 2 }$$ (or 2 {π.