if `loga/(b-c)=logb/(c-a)=logc/(a-b)` then find the value of `a^ab^bc^c`

If (loga)/(b-c) = (logb)/(c-a) = (logc)/(a-b) , then prove that a^(a)b^(b)c^(c)=1 .

loga/(y-z)=logb/(z-x)=logc/(x-y) then value of abc=

If loga/(b-c) = logb/(c-a) = logc/(a-b) , then a^(b+c).b^(c+a).c^(a+b) =

If loga/(b-c) = logb/(c-a) = logc/(a-b) , then a^(b+c).b^(c+a).c^(a+b) =

IF a^x=b,b^y=c,c^z=a,x=log_b a^(k1),y=log_c b^(k2),z=log_a c^(k3) , find the minimum value of 3k_1+6k_2+12k_3 .

If a:b=3:1 and b:c=5:1 , then find the value of ((a^3)/(15b^2c))^3

If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lambdaa^2b^2c^2, then find the value of lambda

If log_b a log_c a+log_a blog_c b+log_a clog_b c=3(where a,b,c are different positive real number !=1) then find the value of abc

if [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=lambda a^2b^2c^2 then find the value of lambda