If x,y,z are in G.P then show that `log x,log y,log z` are in A.P.`(x>0,y>0,z>0)`.

If x,y,z are in G.P then show that log_a x+log_a z=2/(log_y a),(x>0,y>0,z>0) .

If 1/2 , x, y, z, 128 are in G.P., then find x,y,z,

If a,b,c are in G.P and a^(1/x)=b^(1/y)=c^(1/z) then prove that x,y,z are in A.P.

Prove that log_a x.log_b y=log_b x.log_a y

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

x and y are two positive integers such that 2,x, y are in A.P. and x, y, 9 are in G.P. then show that -x= 4, y= 6.

The numbers x, 8, y (xney) are in G.P. and the numbers x, y,-8 are in A.P., then show that x = 16, y = 4

If x, y, z,w in are in G.P., prove that (xy-wz)/(y^2-z^2)=(x+z)/y .

If x,y,z are in G.P and p,q,r are in A.P then prove that x^(q-r) y^(r-p) z^(p-q)=1 .

If x^2+y^2=7xy ,then prove that log(x+y)=log3+1/2(logx+logy)