Algebra
# Exponential Functions

What is the sum of all integer values of \(x\) such that

\[ (x^2-17x+71)^{(x^2-34x+240)} =1 ? \]

**Details and assumptions**

\(x\) can be a negative integer. Since the exponent is an integer, the value is still well defined.

\(0^0\) is undefined.

\[\Large a^{(a-1)^{(a-2)}} = a^{a^2-3a+2}\]

Find the sum of all positive integers \(a\) that satisfy the equation above.

Note: \(x\) is a real number.

In England, with respect to the initial population each year, the death rate is \(\frac{1}{46}\) and the birth rate is \(\frac{1}{33}.\)

If there were no emigration, how many years would it take for the population to double?

Note: Round up your answer.

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