[" (vi) ",(1)/(1+log_(b)a+log_(b)c)+(1)/(1+log_(c)a+log_(c)b)+(1)/(1+log_(a)b+log_(a)c)]

1/(1 + log_(b) a + log_(b) c)+ 1/(1 + log_(c)a + log_(c)b) + 1/(1 + log_(a)b + log_(a) c) has the value equal to

( 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

(1)/(1+log_(b)a+log_(b)c)+(1)/(1+log_(c)a+log_(c)b)+(1)/(1+log_(a)b+log_(a)c) has the value equal to

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

(1+log_(c)a)log_(a)x*log_(b)c=log_(b)x log_(a)x

If a,b,c be three such positive numbers (none of them is 1) that (log_(b)a log_(c )a-log_(a)a) + (log_(a)b log_(c )b-log_(b)b) + (log_(a)c log_(b)c-log_(c )c) = 0 , the prove that abc = 1.

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