Problem: The set of x-values satisfying the equation xlog10x=100x3 consists of:
Answer Choices:
A. 101, only
B. 10 , only
C. 100 , only
D. 10 or 100 , only
E. more than two real numbers
Solution:
Take logarithms of both sides to the base 10 .
(log10x)(log10x)=3log10x−log10100 or
(log10x)2−3log10x+2=0
Solve this equation as a quadratic equatic : letting y=log10x.
y2−3y+2=0,y=2 or 1∴log10x=2 or 1
∴x=102=100 or x=101=10