Prove that, `|{:(1,log_xy,log_xz),(log_xz,1,log_yz),(log_zx,log_zy,1):}|=0`

prove that, |{:(" "1,log_xy,log_xz),(log_yx," "1,log_yz),(log_zx,log_zy," "1):}|=0

Prove that |[1,log_xy,log_xz],[log_yx,1,log_yz],[log_zx,log_zy,1]|=0

|{:(log_x xyz,log_xy,log_xz),(log_yxyz,1,log_yz),(log_zxyz,log_zy,1):}|=0

Prove that , |[1,log_x^y,log_x^z],[log_y^x,1,log_y^z],[log_z^x,log_z^y,1]|=0

If x, y and z be greater than 1, then the value of |(1,log_(x)y,log_(x)z),(log_(y)x,1,log_(y)z),(log_(z)x,log_(z)y,1)| is

Prove that, log_(2)2=1

Prove that ln(1+x) 0.

Show that |[1,log_ab,log_ac],[log_ba,1,log_bc],[log_ca,log_cb,1]|=0 ,(a>0,b>0,c>0)

Prove that log_(1/y)x xx log_(1/z)yxx log_(1/x)z=-1

Prove that log_(2)log_(2)log_(4)256+2log_(sqrt2)2=5