Problem: If all the logarithms are real numbers, the equality log(x+3)+log(x−1)=log(x2−2x−3) is satisfied for:
Answer Choices:
A. all real values of x
B. no real values of x
C. all real values of x except x=0
D. no real values of x except x=0
E. all real values of x except x=1
Solution:
log(x+3)+log(x−1)=log(x2−2x−3)∴log(x+3)(x−1)=log(x2−2x−3). ∴x2+2x−3=x2−2x−3,x=0. But when x=0, neither log(x−1) nor log(x2−2x−3) is a real number.