`1/(1+log_b a+log_b c)+1/(1+log_c a+log_c b)+1/(1+log_a b+log_a c)`

( Prove that )/(1+log_(b)a+log_(b)c)+(1)/(1+log_(c)a+log_(c)b)+(1)/(1+log_(a)b+log_(a)c)=1

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 log_(b) a. log_(c ) a + log_(a) b. log_(c ) b + log_(a) c. log_(b) c = 3 (where a, b, c are different positive real number ne 1 ), then find the value of a b c.

Show that log_(b)a log_(c)b log_(a)c=1

If a,b,c are non-zero and different from 1, then the value of |{:( log _(a) 1 , log _(a) b , log _(a) c ), ( log _(a ) ((1)/(b)), log _(b) 1 ,log_(a) ((1)/(c))), ( log _(a) ((1)/(c)) ,log _(a)c, log _(c) 1):}| is

If (log)_b a(log)_c a+(log)_a b(log)_c b+(log)_a c(log)_bc=3 (where a , b , c are different positive real numbers !=1), then find the value of a b c .

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 (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

The value of 1/ ( 1+ log_(ab)c) + 1/(1+ log_(ac)b) + 1/ ( 1+ log_(bc)a) equals

Simplify: 1/(1+(log)_a b c)+1/(1+(log)_b c a)+1/(1+(log)_c a b)