If `a ,\ b ,\ c` are in G.P. prove that `1/((log)_a m),1/((log)_b m),1/((log)_c m)` are in A.P.

Prove that ((log)_a N)/((log)_(a b)N)=1+(log)_a b

Prove that ((log)_a N)/((log)_(a b)N)=1+(log)_a b

If a >1,b >1 and c >1 are in G.P. then show that 1/(1+(log)_e a),1/(1+(log)_e b), a n d1/(1+(log)_e c) are in H.P.

If a,b,c are in G.P.,then prove that log a^(n),log b^(n),log c^(n)quad are in A.P.

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

If a,b,c are in G.P., prove that: log_ax,log_bx,log_cx are in H.P.

If a>1,b>1 and c>1 are in G.P.then show that (1)/(1+(log)_(e)a),(1)/(1+(log)_(e)b), and (1)/(1+(log)_(e)c) are in H.P.

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

If a (b +c), b (c+a) , c (a +b) are in A.P. , prove that (1)/(a), (a)/(b), (1)/(c ) are also ln A.P.