Not A: We can't have [tex]x=0[/tex] because [tex]\log0[/tex] is undefined for a logarithm of any base.
B is true: [tex]\log1=0[/tex] for any base.
Not C: If [tex]x=b^c[/tex], then [tex]\log_bb^c=c[/tex], but [tex]\log_cb^c=c\log_bc[/tex] which only reduces to [tex]c[/tex] if [tex]\log_bc=1[/tex]. This can only happen if [tex]b=c[/tex], however, but we've assumed otherwise.
Not D: The reasoning for C not being correct is enough to rule out this possibility.
