Problem:
The product of all real roots of the equation xlog10x=10 is
Answer Choices:
A. 1
B. −1
C. 10
D. 10−1
E. none of these
Solution:
Given xlog11x=10, take logs base 10 of both sides:
(log10x)(log10x)log10xx=1,=±1,=10,10−1
Neither solution is extraneous. Thus the product of the roots is 1.