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Found: 2
Problem #PRU-60864
Problems Algebra and arithmetic Exponential functions and logarithms Exponential functions and logarithms (other) Calculus Real numbers Rational and irrational numbers Number theory. Divisibility The fundamental theorm of arithmetic. Prime factorisation.
 14–16  3.0

For what natural numbers \(a\) and \(b\) is the number \(\log_{a} b\) rational?

Problem #PRU-109438
Problems Calculus Functions of one variable. Continuity Certain properties of a function and recurrence relations. Algebra and arithmetic Exponential functions and logarithms Exponential functions and logarithms (other)
 13–16  3.0

The function \(f\) is such that for any positive \(x\) and \(y\) the equality \(f (xy) = f (x) + f (y)\) holds. Find \(f (2007)\) if \(f (1/2007) = 1\).

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