Prove that `log_b a * log_c b * log_d c = log_d a`

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

If a,b,c are in G.P.prove that log a,log b,log c are in A.P.

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 that: (log_(a)(log_(b)a))/(log_(b)(log_(a)b))=-log_(a)b

Prove that: log_(a)x=log_(b)x xx log_(c)b xx...xx log_(n)m xx log_(a)n

If x = log_(c) b + log_(b) c, y = log_(a) c + log_(c) a, z = log_(b) a + log_(a) b, then x^(2) + y^(2) + z^(2) - 4 =

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 in G.P.,prove that: log_(a)x,log_(b)x,log_(c)x are in H.P.