Prove that the value of each the following determinants is zero: `|logxlogylogz log2x log2y log2z log3x log3y log3z|`

For positive numbers x,y and z, the numerical value of the determinant det[[log_(x)y,log_(x)zlog_(y)x,1,log_(y)zlog_(z)x,log_(z)y,1]]

Express the following as a single logarithm. 1/3 log x - 8/5 log y + 7/2 log z

Suppose x,y,z>1 then least value of log(xyz)[(log x)/(log y log z)+(log y)/(log x log z)+(log z)/(log x log y)]

prove that x^(log y-log z)*y^(log z-log x)*z^(log x-log y)=1

For positive numbers x, y and z, the numerical value of the determinant |{:(1,"log"_(x)y, "log"_(x)z),("log"_(y)x, 1, "log"_(y)z),("log"_(z)x, "log"_(z)y, 1):}| is……

For positive numbers x,y,s the numberical value of the determinant |{:(1,log_(x)y,log_(x)z),(log_(y)x,3,log_(y)z),(log_(z)x,log_(z)y,5):}| is

Write each of the following as single logarithm: (a) 1+ log_(2) 5" "(b) 2- log_(3) 7 (c) 2log_(10) x+3 log_(10) y - 5 log_(10) z

Find the value of (x^(log y - log z))(y^(log z-log x))(z^(log x - log y))