If `2^x=4^y=8^z` then find `x:y:z`

If 2^(x)=4^(y)=8^(z) and (1)/(2x)+(1)/(4y)+(1)/(8z)=4 find the value of x.

If [x y4z+6x+y]=[8w0 6] , then find the values of x ,\ y ,\ z\ a n d\ w .

If x,y,z in R and |{:(x,y^2,z^3),(x^4,y^5,z^6),(x^7,y^8,z^9):}|=2 then find the value of |{:(y^5z^6(z^3-y^3),x^4z^6(x^3-z^3),x^4y^5(y^3-x^3)),(y^2z^3(y^6-z^6),xz^3(z^6-x^6), xy^2(x^6-y^6)),(y^2z^3(z^3-y^3),xz^3(x^3-z^3),xy^2(y^3-x^3)):}|

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(z y-z)+cot^(-1)(z x+1)/(z-x)

If 9(27)^(x^2+y+z)+9(27)^(x+y+z^2)+9(27)^(x+y^2+z)=11 then find the number of possible triplet (x ,y ,z)dot

If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(y-z)+cot^(-1)(z x+1)/(z-x)

If [(x,3x-y),(2x+z,3y-w)]=[(3,2),(4,7)], then find x+y+z+w.

If z_1=9y^2-4-10ix, z_2=8y^2-20i, where z_1=overline z_2, then find z=x+iy

If X = 5Y = 8Z, find X:Y:Z.

If x+y+z=8\ \ a n d\ \ \ x y+y z+z x=20 , find the value of x^3+y^3+z^3-3x y z