1,log x base y,log y base z,-15log z base x are in AP ..,then??

Answer 1

there is a common difference, so
log_y(x) - 1 = log_z(y)-log_y(x)
log_z(y)-log_y(x) = -15log_x(z) - log_z(y)

Not sure just where you want to go with this, since you only have two equations in three unknowns, but if you play around a bit, you should arrive at the fact that both equations work if

x = 1/y = z^3

Answer 2

Useless answer