`a^(logb-logc)*b^(logc-loga)*c^(loga-logb)` has a value of :

If a, b, c are positive real numbers, then the minimum value of a^(logb-logc)+b^(logc-loga)+c^(loga-logb) is

If a, b, c are positive real numbers, then the minimum value of a^(logb-logc)+b^(logc-loga)+c^(loga-logb) is

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

If log(2a-3b)=loga-logb, then a=

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

If a, b, c are distinct positive real numbers each different from unity such that (log_b a.log_c a -log_a a) + (log_a b.log_c b-logb_ b) + (log_a c.log_b c - log_c c) = 0, then prove that abc = 1.

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

If (log_a N)/(log_c N)=(log_a N-log_b N)/(log_b N-log_c N) where N>0 and N!=1 a,b,c>0 and not equal to 1 , then prove that b^2=ac

Q. If log_x a, a^(x/2) and log_b x are in G.P. then x is equal to (1) log_a(log_b a) (2) log_a(log_e a)+log_a log_b b (3) -log_a(log_a b) (4) none of these

Suppose a,b,c,gt0 and a,b,c are the pth, qth, rth terms of a G.P. Let Delta=|(1,p,loga),(1,q,logb),(1,r,logc)| the numerical value of Delta is