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

If a,b,c are distinct real number different from 1 such that (log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0 , then abc is equal to

Let a,b" and "c are distinct positive numbers,none of them is equal to unity such that log _(b)a .log_(c)a+log_(a)b*log_(c)b+log_(a)c*log_(b)c-log_(b)a sqrt(a)*log_(sqrt(c))b^(1/3)*log_(a)c^(3)=0, then the value of abc is -

If in a right angled triangle, a and b are the lengths of sides and c is the length of hypotenuse and c-b ne 1, c+b ne 1 , then show that log_(c+b)a+log_(c-b)a=2log_(c+b)a.log_(c-b)a.

Given a^2+b^2=c^2 . Prove that log_(b+c)a+log_(c-b)a=2 log_(c+b)a.log_(c-b)a,forallagt0,ane1 c-bgt0 , c+bgt0 c-bne1 , c+bne1 .

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :

If in a right angle triangle,a and b are the length of the sides and and c is the length of the hypotenuse and c-b!=1,c+b!=1 then show that log_(c+b)(a)+log_(c-b)(a)=2log_(c+b)(a)log_(c-b)(a)

If a,b,c are distinct positive real numbers each different from unity such that (log_(a)a.log_(c)a-log_(a)a)+(log_(a)b*log_(c)b-log b_(b))+(log_(a)c.log_(a)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.