Short Calculus pp 116-133 | Cite as

Exponents and Logarithms

  • Serge Lang
Part of the Undergraduate Texts in Mathematics book series (UTM)


We remember that we had trouble at the very beginning with the function 2 x (or 3 x , or 10 x ). It was intuitively very plausible that there should be such functions, satisfying the fundamental equation
$$ 2^{x + y} = 2^x 2^y $$
for all numbers x, y, and 20 = 1, but we had difficulties in saying what we meant by \( 2^{\sqrt 2 } \) (or 2 π ).


Positive Integer Tangent Line Chain Rule Original Amount Geometric Intuition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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