Log First

Algebra Level 5

If \(\ln x_1+ \ln x_2 + \cdots + \ln x_n =1\), where each \(\ln x_i \) is a proper fraction. Find the greatest integral value of \[\ln x -\lfloor \ln x_1 \times \ln x \rfloor -\lfloor \ln x_2 \times \ln x \rfloor -\cdots-\lfloor \ln x_n \times \ln x \rfloor\]

where \(n = 101 \), and \(\ln x \) is an integer.

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

×

Problem Loading...

Note Loading...

Set Loading...