Question

Given that A > B > C and A^60=B^t=C^120.If logA, logB and logC are in Arithmetic Progression, then what is the value of 't'?

Answer 1

Step-by-step explanation:

Correct option is C)

loga,logb,logc are in A.P.

⇒2logb=loga+logc

⇒logb

2

=log(ac)

⇒b

2

=ac⇒a,b,c are in G.P.

loga−log2b,log2b−log3c,log3c−loga are in A.P.

⇒2(log2b−log3c)=(loga−log2b)+(log3c−loga)

⇒3log2b=3log3c⇒2b=3c

Now,

b2=ac⇒b 2=a.

32b⇒b= 32a,c= 94a

i.e., a=a,b= 32a,c= 94a⇒a:b:c=1: 32: 94

=9:6:4

Since, sum of any two is greater than the 3

rd

,a,b,c form a triangle.