A Trivial Problem

Algebra Level 3

Let f ( x ) = ∣ log ⁡ 3 x ∣ f(x)=|\log_{3}x| , m , n ∈ R m,n \in \mathbb R , 0 < m < n 0<m<n , f ( m ) = f ( n ) f(m)=f(n) .

If the maximum value of f ( x ) f(x) at [ m 2 , n ] [m^2,n] is 2 2 , what is n m \dfrac{n}{m} ?


The answer is 9.

Alice Smith by Alice Smith , 20, China

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1 solution

From the definition of f ( x ) f(x) and the given condition we get m = m= 1 n \dfrac{1}{n} . In the given interval, maximum of f ( x ) f(x) is 2. This implies n = 3 n=3 and n m \dfrac{n}{m} =9

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