a,b,c are positive numbers such that they are in increasing Geometric progression then how many such numbers are there in (loga+logb+logc)/6 =log6
Choose the correct choice from the following answers.
A) 1  B) 2  C) 3  D) 4  E) 5
given that a,b,c are in gp   so b/a=c/b =&gt;b^2=ac   (loga+logb+logc)/6=log6   =&gt;log(abc)=6*log6   =&gt;log(ac*b)=log(6^6)   =&gt;log(b^3)=log(6^6)   =&gt;b^3=6^6=&gt;b^3=(6^2)^3   =&gt;b=6^2=36   it means a=2,c=18 or a=3 c=12 or a=4 c=9 or a=6 c=6.   hence there are four such numbers   ANSWER:4
<result>D</result>
a,b,c are positive numbers such that they are in increasing Geometric progression then how many such numbers are there in (loga+logb+logc)/6 =log6