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

Show that log_(b)a xx log_(c )b xx log_(d)c = log_(d)a .

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 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_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0 , then abc is equal to

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.

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.

Prove that log_(b^3)a xx log_(c^3)b xx log_(a^3)c = 1/27

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.

If a, b, c are distinct positive numbers each being different from 1 such 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 , then abc is a)0 b)e c)1 d)2