Problem: If logMβN=logNβM,Mξ =N,MN>0,Mξ =1,Nξ =1, then MN equals:
Answer Choices:
A. 21β
B. 1
C. 2
D. 10
E. a number greater than 2 and less than 10
Solution:
Let logMβN=x; then logNβM=logMβN1β=x1β.β΄x2=1,x=+1 or -1 . If x=1 then M=N, but this contradicts the given Mξ =N. If x=β1, then N=Mβ1β΄MN=1
or
Let logMβN=x=logNβMβ΄N=Mx and M=Nxβ΄(Mx)x=Nx=M
β΄xβ
x=1β΄x=1 (rejected) or x=β1β΄N=Mβ1β΄NM=1