Log First

Algebra Level 5

If lnx1+lnx2++lnxn=1\ln x_1+ \ln x_2 + \cdots + \ln x_n =1, where each lnxi\ln x_i is a proper fraction. Find the greatest integral value of lnxlnx1×lnxlnx2×lnxlnxn×lnx\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=101n = 101 , and lnx\ln x is an integer.

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

×

Problem Loading...

Note Loading...

Set Loading...