" 5."|[1,log_(b)a],[log_(a)b,1]|

If a,b,c gt1 then Delta=|(log_(a)(abc),log_(a)b,log_(a)c),(log_b(abc),1,log_(b)c),(log_(c)(abc),log_(c)b,1)| equals

If a>1,b>1, then the minimum value of log_(b)a+log_(a)b is

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

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

( 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 agt1,bgt1,cgt1,dgt1 then the minimum value of log_(b)a+log_(a)b+log_(d)c+log_(c)d , is

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.

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .