Problem: It is possible to choose x>32​ in such a way that the value of log10​(x2+3) −2log10​x is:
Answer Choices:
A. negative
B. zero
C. one
D. smaller than any positive number that might be specified
E. greater than any positive number that might be specified
Solution:
log10​(x2+3)−2log10​x=log10​x2x2+3​=log10​(1+x23​). For a sufficiently large value of x,x23​ may be made less than a specified positive number N and so log10​(1+x23​) may be made less than the specified positive number log10​(1+N). Challenge: If, in the problem, the condition x>21​ were given instead of x>32​, show that then (B) would also be an acceptable answer.