If x,y,z are in GP and ax=by=cz, then
logac=logba
logba=logcb
logcb=logac
None of these
Explanation for the correct answer:
Let ax=by=cz=λ say
Taking logarithm we get
logax=logby=logcz=logλ
⇒xloga=ylogb=zlogc=logλ ...∵logmn=n×logm
⇒x=logλloga ...(i)
⇒y=logλlogb ...(ii)
⇒ z=logλlogc ...(iii)
We know that x,y,z are in a geometric progression
⇒y2=xz
From (i),(ii),(iii) we get
⇒ logλlogb2=logλloga×logλlogc
⇒1logb×logb=1loga×logc
⇒ logalogb=logblogc ...∵logxlogy=logyx
⇒ logba=logcb
Hence, option (B) is the correct answer.