Question

How exactly do these procedures work?

(define (square x)
(exp (double (log x))))

(define (double x) (+ x x))

Answer 1

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Answer 2

Pretty staightforward; remember how logs/exponents work:

\[\begin{align}
exp(double (log x)) &= e^{2 \ln x}\\
&= e^{\ln x^2}\\
&= x^2
\end{align}\]

Have a look at http://en.wikipedia.org/wiki/Logarithm for more.