If $(1), (log_yx), (log_zy), (-15log_xz)$ are in AP then...
(A)$z^3=x$
(B)$x=y^{-1}$
(C)$z^{-3}=y$
(D)$x=y^{-1}=z^3$
(Multiple answers may be correct)
I tried many approaches, one of them being:
$1+log_zy=2log_yx$
$log_zz+log_zy=log_yx^2$
$log_z(yz)=log_yx^2$
But the fact that the bases are different is causing the main problem as I don't know how to proceed further. It would be great if anybody could give me a hint for solving such questions.