a,b,c > 0

 

log a + log c = 2log b                                   

=> ac = b^2............................ 1 

and

                                                          as log a+ log b= log ba...and

                                                              log a - log b = log a/b

log a/2b + log 3c/a = log 2b/3c

=> log 3c/2b = log 2b/3c

=> 2b= 3c as all r postive............. 2

 

solving frm 1 and 2

4a= 6b= 9c=k

 

so a=k/4= 36m/4=9m.... b=k/6= 6m.... c = 4m...whre let k= 36m( lcm of 4,6,9)

 

now sum of any two > third

lik a+b>c or

b+c> a

c+a> b

so these are sides of a triangle

 

 

getting unusual ans.

hope its rit

 

 

Cheers!!!