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`1/log_a(a b)+1/log_b(a b)=1`

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(1)/(log_(a)(ab)+(1)/(log_(b)(ab)=1))

Prove that 1/(log_(a/b) x)+1/(log_(b/c) x)+1/(log_(c/a) x)=0

If a,b,c are in GP then 1/(log_(a)x), 1/(log_(b)x), 1/(log_( c)x) are in:

2^((sqrt(log_a(ab)^(1/4)+log_b(ab)^(1/4))-sqrt(log_a(b/a)^(1/4)+log_b(a/b)^(1/4)))sqrt(log_a(b)) =

(1/(log_(a)bc+1) + 1/(log_(b) ac +1) + 1/(log_(c)ab+1)+1) is equal to:

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

2^((sqrt(log_a(ab)^(1//4)+log_b(ab)^(1//4))-sqrt(log_a(b/a)^(1//4)+log_b(a/b)^(1//4))) sqrt(log_a(b)) =

2^((sqrt(log_a(ab)^(1//4)+log_b(ab)^(1//4))-sqrt(log_a(b/a)^(1//4)+log_b(a/b)^(1//4))) sqrt(log_a(b)) =